Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.0% → 53.9%

Time: 21.7s

Alternatives: 38

Speedup: 4.2×

• 88.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 53.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := a \cdot b - c \cdot i\\ t_3 := c \cdot y4 - a \cdot y5\\ t_4 := j \cdot t - k \cdot y\\ t_5 := -1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, t\_4, y0 \cdot t\_1\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ t_6 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y5 \leq -4.8 \cdot 10^{+205}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y5 \leq -2.5 \cdot 10^{+27}:\\ \;\;\;\;y0 \cdot \left(\mathsf{fma}\left(-1, y5 \cdot t\_1, c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \mathbf{elif}\;y5 \leq -3 \cdot 10^{-161}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(\mathsf{fma}\left(k, z, \frac{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot t\_4\right)}{y0}\right) - j \cdot x\right)\right)\\ \mathbf{elif}\;y5 \leq 4.6 \cdot 10^{-144}:\\ \;\;\;\;-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot t\_6\right) - y \cdot t\_3\right)\right)\\ \mathbf{elif}\;y5 \leq 4.5 \cdot 10^{-34}:\\ \;\;\;\;-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, t\_2, y3 \cdot t\_6\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.52 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot t\_2\right) - -1 \cdot \left(y3 \cdot t\_3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* a b) (* c i)))
        (t_3 (- (* c y4) (* a y5)))
        (t_4 (- (* j t) (* k y)))
        (t_5
         (*
          -1.0
          (* y5 (- (fma i t_4 (* y0 t_1)) (* a (- (* t y2) (* y y3)))))))
        (t_6 (- (* c y0) (* a y1))))
   (if (<= y5 -4.8e+205)
     t_5
     (if (<= y5 -2.5e+27)
       (*
        y0
        (-
         (fma -1.0 (* y5 t_1) (* c (- (* x y2) (* y3 z))))
         (* b (- (* j x) (* k z)))))
       (if (<= y5 -3e-161)
         (*
          b
          (*
           y0
           (-
            (fma k z (/ (fma a (- (* x y) (* t z)) (* y4 t_4)) y0))
            (* j x))))
         (if (<= y5 4.6e-144)
           (*
            -1.0
            (* y3 (- (fma j (- (* y1 y4) (* y0 y5)) (* z t_6)) (* y t_3))))
           (if (<= y5 4.5e-34)
             (*
              -1.0
              (* z (- (fma t t_2 (* y3 t_6)) (* k (- (* b y0) (* i y1))))))
             (if (<= y5 1.52e+60)
               (*
                y
                (-
                 (fma -1.0 (* k (- (* b y4) (* i y5))) (* x t_2))
                 (* -1.0 (* y3 t_3))))
               t_5))))))))

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 = (a * b) - (c * i);
	double t_3 = (c * y4) - (a * y5);
	double t_4 = (j * t) - (k * y);
	double t_5 = -1.0 * (y5 * (fma(i, t_4, (y0 * t_1)) - (a * ((t * y2) - (y * y3)))));
	double t_6 = (c * y0) - (a * y1);
	double tmp;
	if (y5 <= -4.8e+205) {
		tmp = t_5;
	} else if (y5 <= -2.5e+27) {
		tmp = y0 * (fma(-1.0, (y5 * t_1), (c * ((x * y2) - (y3 * z)))) - (b * ((j * x) - (k * z))));
	} else if (y5 <= -3e-161) {
		tmp = b * (y0 * (fma(k, z, (fma(a, ((x * y) - (t * z)), (y4 * t_4)) / y0)) - (j * x)));
	} else if (y5 <= 4.6e-144) {
		tmp = -1.0 * (y3 * (fma(j, ((y1 * y4) - (y0 * y5)), (z * t_6)) - (y * t_3)));
	} else if (y5 <= 4.5e-34) {
		tmp = -1.0 * (z * (fma(t, t_2, (y3 * t_6)) - (k * ((b * y0) - (i * y1)))));
	} else if (y5 <= 1.52e+60) {
		tmp = y * (fma(-1.0, (k * ((b * y4) - (i * y5))), (x * t_2)) - (-1.0 * (y3 * t_3)));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(a * b) - Float64(c * i))
	t_3 = Float64(Float64(c * y4) - Float64(a * y5))
	t_4 = Float64(Float64(j * t) - Float64(k * y))
	t_5 = Float64(-1.0 * Float64(y5 * Float64(fma(i, t_4, Float64(y0 * t_1)) - Float64(a * Float64(Float64(t * y2) - Float64(y * y3))))))
	t_6 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y5 <= -4.8e+205)
		tmp = t_5;
	elseif (y5 <= -2.5e+27)
		tmp = Float64(y0 * Float64(fma(-1.0, Float64(y5 * t_1), Float64(c * Float64(Float64(x * y2) - Float64(y3 * z)))) - Float64(b * Float64(Float64(j * x) - Float64(k * z)))));
	elseif (y5 <= -3e-161)
		tmp = Float64(b * Float64(y0 * Float64(fma(k, z, Float64(fma(a, Float64(Float64(x * y) - Float64(t * z)), Float64(y4 * t_4)) / y0)) - Float64(j * x))));
	elseif (y5 <= 4.6e-144)
		tmp = Float64(-1.0 * Float64(y3 * Float64(fma(j, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(z * t_6)) - Float64(y * t_3))));
	elseif (y5 <= 4.5e-34)
		tmp = Float64(-1.0 * Float64(z * Float64(fma(t, t_2, Float64(y3 * t_6)) - Float64(k * Float64(Float64(b * y0) - Float64(i * y1))))));
	elseif (y5 <= 1.52e+60)
		tmp = Float64(y * Float64(fma(-1.0, Float64(k * Float64(Float64(b * y4) - Float64(i * y5))), Float64(x * t_2)) - Float64(-1.0 * Float64(y3 * t_3))));
	else
		tmp = t_5;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(-1.0 * N[(y5 * N[(N[(i * t$95$4 + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -4.8e+205], t$95$5, If[LessEqual[y5, -2.5e+27], N[(y0 * N[(N[(-1.0 * N[(y5 * t$95$1), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3e-161], N[(b * N[(y0 * N[(N[(k * z + N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$4), $MachinePrecision]), $MachinePrecision] / y0), $MachinePrecision]), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.6e-144], N[(-1.0 * N[(y3 * N[(N[(j * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$6), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.5e-34], N[(-1.0 * N[(z * N[(N[(t * t$95$2 + N[(y3 * t$95$6), $MachinePrecision]), $MachinePrecision] - N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.52e+60], N[(y * N[(N[(-1.0 * N[(k * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(-1.0 * N[(y3 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -4.79999999999999972e205 or 1.52e60 < y5

   1. Initial program 23.9%

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

   2. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 55.3%

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

   if -4.79999999999999972e205 < y5 < -2.4999999999999999e27

   1. Initial program 25.6%

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

   2. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 35.1%

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

   if -2.4999999999999999e27 < y5 < -2.99999999999999989e-161

   1. Initial program 33.2%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 40.5%

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

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   7. Applied rewrites 44.9%

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

   if -2.99999999999999989e-161 < y5 < 4.6e-144

   1. Initial program 36.3%

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

   2. Taylor expanded in 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 36.9%

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

   if 4.6e-144 < y5 < 4.50000000000000042e-34

   1. Initial program 34.1%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 38.1%

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

   if 4.50000000000000042e-34 < y5 < 1.52e60

   1. Initial program 29.5%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.4%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 2: 44.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := x \cdot y - t \cdot z\\ t_3 := j \cdot x - k \cdot z\\ t_4 := j \cdot t - k \cdot y\\ t_5 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y5 \leq -4.8 \cdot 10^{+205}:\\ \;\;\;\;-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, t\_4, y0 \cdot t\_1\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -2.5 \cdot 10^{+27}:\\ \;\;\;\;y0 \cdot \left(\mathsf{fma}\left(-1, y5 \cdot t\_1, c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot t\_3\right)\\ \mathbf{elif}\;y5 \leq -3 \cdot 10^{-161}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(\mathsf{fma}\left(k, z, \frac{\mathsf{fma}\left(a, t\_2, y4 \cdot t\_4\right)}{y0}\right) - j \cdot x\right)\right)\\ \mathbf{elif}\;y5 \leq 4.6 \cdot 10^{-144}:\\ \;\;\;\;-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot t\_5\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2.4 \cdot 10^{-33}:\\ \;\;\;\;-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot t\_5\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, t\_2, y5 \cdot t\_4\right) - y1 \cdot t\_3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* x y) (* t z)))
        (t_3 (- (* j x) (* k z)))
        (t_4 (- (* j t) (* k y)))
        (t_5 (- (* c y0) (* a y1))))
   (if (<= y5 -4.8e+205)
     (* -1.0 (* y5 (- (fma i t_4 (* y0 t_1)) (* a (- (* t y2) (* y y3))))))
     (if (<= y5 -2.5e+27)
       (* y0 (- (fma -1.0 (* y5 t_1) (* c (- (* x y2) (* y3 z)))) (* b t_3)))
       (if (<= y5 -3e-161)
         (* b (* y0 (- (fma k z (/ (fma a t_2 (* y4 t_4)) y0)) (* j x))))
         (if (<= y5 4.6e-144)
           (*
            -1.0
            (*
             y3
             (-
              (fma j (- (* y1 y4) (* y0 y5)) (* z t_5))
              (* y (- (* c y4) (* a y5))))))
           (if (<= y5 2.4e-33)
             (*
              -1.0
              (*
               z
               (-
                (fma t (- (* a b) (* c i)) (* y3 t_5))
                (* k (- (* b y0) (* i y1))))))
             (* -1.0 (* i (- (fma c t_2 (* y5 t_4)) (* y1 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (x * y) - (t * z);
	double t_3 = (j * x) - (k * z);
	double t_4 = (j * t) - (k * y);
	double t_5 = (c * y0) - (a * y1);
	double tmp;
	if (y5 <= -4.8e+205) {
		tmp = -1.0 * (y5 * (fma(i, t_4, (y0 * t_1)) - (a * ((t * y2) - (y * y3)))));
	} else if (y5 <= -2.5e+27) {
		tmp = y0 * (fma(-1.0, (y5 * t_1), (c * ((x * y2) - (y3 * z)))) - (b * t_3));
	} else if (y5 <= -3e-161) {
		tmp = b * (y0 * (fma(k, z, (fma(a, t_2, (y4 * t_4)) / y0)) - (j * x)));
	} else if (y5 <= 4.6e-144) {
		tmp = -1.0 * (y3 * (fma(j, ((y1 * y4) - (y0 * y5)), (z * t_5)) - (y * ((c * y4) - (a * y5)))));
	} else if (y5 <= 2.4e-33) {
		tmp = -1.0 * (z * (fma(t, ((a * b) - (c * i)), (y3 * t_5)) - (k * ((b * y0) - (i * y1)))));
	} else {
		tmp = -1.0 * (i * (fma(c, t_2, (y5 * t_4)) - (y1 * t_3)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(x * y) - Float64(t * z))
	t_3 = Float64(Float64(j * x) - Float64(k * z))
	t_4 = Float64(Float64(j * t) - Float64(k * y))
	t_5 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y5 <= -4.8e+205)
		tmp = Float64(-1.0 * Float64(y5 * Float64(fma(i, t_4, Float64(y0 * t_1)) - Float64(a * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (y5 <= -2.5e+27)
		tmp = Float64(y0 * Float64(fma(-1.0, Float64(y5 * t_1), Float64(c * Float64(Float64(x * y2) - Float64(y3 * z)))) - Float64(b * t_3)));
	elseif (y5 <= -3e-161)
		tmp = Float64(b * Float64(y0 * Float64(fma(k, z, Float64(fma(a, t_2, Float64(y4 * t_4)) / y0)) - Float64(j * x))));
	elseif (y5 <= 4.6e-144)
		tmp = Float64(-1.0 * Float64(y3 * Float64(fma(j, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(z * t_5)) - Float64(y * Float64(Float64(c * y4) - Float64(a * y5))))));
	elseif (y5 <= 2.4e-33)
		tmp = Float64(-1.0 * Float64(z * Float64(fma(t, Float64(Float64(a * b) - Float64(c * i)), Float64(y3 * t_5)) - Float64(k * Float64(Float64(b * y0) - Float64(i * y1))))));
	else
		tmp = Float64(-1.0 * Float64(i * Float64(fma(c, t_2, Float64(y5 * t_4)) - Float64(y1 * t_3))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -4.8e+205], N[(-1.0 * N[(y5 * N[(N[(i * t$95$4 + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.5e+27], N[(y0 * N[(N[(-1.0 * N[(y5 * t$95$1), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3e-161], N[(b * N[(y0 * N[(N[(k * z + N[(N[(a * t$95$2 + N[(y4 * t$95$4), $MachinePrecision]), $MachinePrecision] / y0), $MachinePrecision]), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.6e-144], N[(-1.0 * N[(y3 * N[(N[(j * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.4e-33], N[(-1.0 * N[(z * N[(N[(t * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(i * N[(N[(c * t$95$2 + N[(y5 * t$95$4), $MachinePrecision]), $MachinePrecision] - N[(y1 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -4.79999999999999972e205

   1. Initial program 23.5%

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

   2. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 59.9%

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

   if -4.79999999999999972e205 < y5 < -2.4999999999999999e27

   1. Initial program 25.6%

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

   2. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 35.1%

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

   if -2.4999999999999999e27 < y5 < -2.99999999999999989e-161

   1. Initial program 33.2%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 40.5%

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

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   7. Applied rewrites 44.9%

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

   if -2.99999999999999989e-161 < y5 < 4.6e-144

   1. Initial program 36.3%

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

   2. Taylor expanded in 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 36.9%

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

   if 4.6e-144 < y5 < 2.4e-33

   1. Initial program 34.0%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 38.3%

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

   if 2.4e-33 < y5

   1. Initial program 25.6%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 40.1%

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

Alternative 3: 43.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)\\ t_2 := j \cdot t - k \cdot y\\ t_3 := y4 \cdot \left(\mathsf{fma}\left(b, t\_2, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y4 \leq -5.8 \cdot 10^{+59}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y4 \leq -5.5 \cdot 10^{-82}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot t\_2\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -1.6 \cdot 10^{-286}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 2.7 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(y, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 1.15 \cdot 10^{+202}:\\ \;\;\;\;b \cdot \left(y \cdot \mathsf{fma}\left(-1, k \cdot y4, a \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* z (fma -1.0 (* y0 y3) (* i t)))))
        (t_2 (- (* j t) (* k y)))
        (t_3
         (*
          y4
          (-
           (fma b t_2 (* y1 (- (* k y2) (* j y3))))
           (* c (- (* t y2) (* y y3)))))))
   (if (<= y4 -5.8e+59)
     t_3
     (if (<= y4 -5.5e-82)
       (*
        -1.0
        (*
         i
         (-
          (fma c (- (* x y) (* t z)) (* y5 t_2))
          (* y1 (- (* j x) (* k z))))))
       (if (<= y4 -1.6e-286)
         t_1
         (if (<= y4 2.7e-56)
           (*
            x
            (-
             (fma y (- (* a b) (* c i)) (* y2 (- (* c y0) (* a y1))))
             (* j (- (* b y0) (* i y1)))))
           (if (<= y4 6.5e+80)
             t_1
             (if (<= y4 1.15e+202)
               (* b (* y (fma -1.0 (* k y4) (* a x))))
               t_3))))))))

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 = c * (z * fma(-1.0, (y0 * y3), (i * t)));
	double t_2 = (j * t) - (k * y);
	double t_3 = y4 * (fma(b, t_2, (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	double tmp;
	if (y4 <= -5.8e+59) {
		tmp = t_3;
	} else if (y4 <= -5.5e-82) {
		tmp = -1.0 * (i * (fma(c, ((x * y) - (t * z)), (y5 * t_2)) - (y1 * ((j * x) - (k * z)))));
	} else if (y4 <= -1.6e-286) {
		tmp = t_1;
	} else if (y4 <= 2.7e-56) {
		tmp = x * (fma(y, ((a * b) - (c * i)), (y2 * ((c * y0) - (a * y1)))) - (j * ((b * y0) - (i * y1))));
	} else if (y4 <= 6.5e+80) {
		tmp = t_1;
	} else if (y4 <= 1.15e+202) {
		tmp = b * (y * fma(-1.0, (k * y4), (a * x)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(z * fma(-1.0, Float64(y0 * y3), Float64(i * t))))
	t_2 = Float64(Float64(j * t) - Float64(k * y))
	t_3 = Float64(y4 * Float64(fma(b, t_2, Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))))
	tmp = 0.0
	if (y4 <= -5.8e+59)
		tmp = t_3;
	elseif (y4 <= -5.5e-82)
		tmp = Float64(-1.0 * Float64(i * Float64(fma(c, Float64(Float64(x * y) - Float64(t * z)), Float64(y5 * t_2)) - Float64(y1 * Float64(Float64(j * x) - Float64(k * z))))));
	elseif (y4 <= -1.6e-286)
		tmp = t_1;
	elseif (y4 <= 2.7e-56)
		tmp = Float64(x * Float64(fma(y, Float64(Float64(a * b) - Float64(c * i)), Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) - Float64(j * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y4 <= 6.5e+80)
		tmp = t_1;
	elseif (y4 <= 1.15e+202)
		tmp = Float64(b * Float64(y * fma(-1.0, Float64(k * y4), Float64(a * x))));
	else
		tmp = t_3;
	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[(c * N[(z * N[(-1.0 * N[(y0 * y3), $MachinePrecision] + N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(N[(b * t$95$2 + 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, -5.8e+59], t$95$3, If[LessEqual[y4, -5.5e-82], N[(-1.0 * N[(i * N[(N[(c * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.6e-286], t$95$1, If[LessEqual[y4, 2.7e-56], N[(x * N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.5e+80], t$95$1, If[LessEqual[y4, 1.15e+202], N[(b * N[(y * N[(-1.0 * N[(k * y4), $MachinePrecision] + N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -5.79999999999999981e59 or 1.15e202 < y4

   1. Initial program 22.4%

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

   2. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 55.6%

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

   if -5.79999999999999981e59 < y4 < -5.4999999999999998e-82

   1. Initial program 33.2%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 38.8%

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

   if -5.4999999999999998e-82 < y4 < -1.60000000000000003e-286 or 2.69999999999999995e-56 < y4 < 6.4999999999999998e80

   1. Initial program 33.8%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 39.9%

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

   5. Taylor expanded in c around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 28.2

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

   7. Applied rewrites 28.2%

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

   if -1.60000000000000003e-286 < y4 < 2.69999999999999995e-56

   1. Initial program 36.0%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 39.4%

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

   if 6.4999999999999998e80 < y4 < 1.15e202

   1. Initial program 24.2%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 39.6%

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

   5. Taylor expanded in y around inf

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + \color{blue}{a \cdot x}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(y \cdot \mathsf{fma}\left(-1, k \cdot \color{blue}{y4}, a \cdot x\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(y \cdot \mathsf{fma}\left(-1, k \cdot y4, a \cdot x\right)\right) \]

      4. lower-*.f64 32.6

         \[\leadsto b \cdot \left(y \cdot \mathsf{fma}\left(-1, k \cdot y4, a \cdot x\right)\right) \]

   7. Applied rewrites 32.6%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1, k \cdot y4, a \cdot x\right)}\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 42.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - t \cdot z\\ t_2 := j \cdot t - k \cdot y\\ t_3 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y5 \leq -5 \cdot 10^{+48}:\\ \;\;\;\;-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, t\_2, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -3 \cdot 10^{-161}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(\mathsf{fma}\left(k, z, \frac{\mathsf{fma}\left(a, t\_1, y4 \cdot t\_2\right)}{y0}\right) - j \cdot x\right)\right)\\ \mathbf{elif}\;y5 \leq 4.6 \cdot 10^{-144}:\\ \;\;\;\;-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot t\_3\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2.4 \cdot 10^{-33}:\\ \;\;\;\;-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot t\_3\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, t\_1, y5 \cdot t\_2\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* t z)))
        (t_2 (- (* j t) (* k y)))
        (t_3 (- (* c y0) (* a y1))))
   (if (<= y5 -5e+48)
     (*
      -1.0
      (*
       y5
       (-
        (fma i t_2 (* y0 (- (* k y2) (* j y3))))
        (* a (- (* t y2) (* y y3))))))
     (if (<= y5 -3e-161)
       (* b (* y0 (- (fma k z (/ (fma a t_1 (* y4 t_2)) y0)) (* j x))))
       (if (<= y5 4.6e-144)
         (*
          -1.0
          (*
           y3
           (-
            (fma j (- (* y1 y4) (* y0 y5)) (* z t_3))
            (* y (- (* c y4) (* a y5))))))
         (if (<= y5 2.4e-33)
           (*
            -1.0
            (*
             z
             (-
              (fma t (- (* a b) (* c i)) (* y3 t_3))
              (* k (- (* b y0) (* i y1))))))
           (*
            -1.0
            (* i (- (fma c t_1 (* y5 t_2)) (* y1 (- (* j x) (* k z))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y) - (t * z);
	double t_2 = (j * t) - (k * y);
	double t_3 = (c * y0) - (a * y1);
	double tmp;
	if (y5 <= -5e+48) {
		tmp = -1.0 * (y5 * (fma(i, t_2, (y0 * ((k * y2) - (j * y3)))) - (a * ((t * y2) - (y * y3)))));
	} else if (y5 <= -3e-161) {
		tmp = b * (y0 * (fma(k, z, (fma(a, t_1, (y4 * t_2)) / y0)) - (j * x)));
	} else if (y5 <= 4.6e-144) {
		tmp = -1.0 * (y3 * (fma(j, ((y1 * y4) - (y0 * y5)), (z * t_3)) - (y * ((c * y4) - (a * y5)))));
	} else if (y5 <= 2.4e-33) {
		tmp = -1.0 * (z * (fma(t, ((a * b) - (c * i)), (y3 * t_3)) - (k * ((b * y0) - (i * y1)))));
	} else {
		tmp = -1.0 * (i * (fma(c, t_1, (y5 * t_2)) - (y1 * ((j * x) - (k * z)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y) - Float64(t * z))
	t_2 = Float64(Float64(j * t) - Float64(k * y))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y5 <= -5e+48)
		tmp = Float64(-1.0 * Float64(y5 * Float64(fma(i, t_2, Float64(y0 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(a * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (y5 <= -3e-161)
		tmp = Float64(b * Float64(y0 * Float64(fma(k, z, Float64(fma(a, t_1, Float64(y4 * t_2)) / y0)) - Float64(j * x))));
	elseif (y5 <= 4.6e-144)
		tmp = Float64(-1.0 * Float64(y3 * Float64(fma(j, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(z * t_3)) - Float64(y * Float64(Float64(c * y4) - Float64(a * y5))))));
	elseif (y5 <= 2.4e-33)
		tmp = Float64(-1.0 * Float64(z * Float64(fma(t, Float64(Float64(a * b) - Float64(c * i)), Float64(y3 * t_3)) - Float64(k * Float64(Float64(b * y0) - Float64(i * y1))))));
	else
		tmp = Float64(-1.0 * Float64(i * Float64(fma(c, t_1, Float64(y5 * t_2)) - Float64(y1 * Float64(Float64(j * x) - Float64(k * z))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -5e+48], N[(-1.0 * N[(y5 * N[(N[(i * t$95$2 + N[(y0 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3e-161], N[(b * N[(y0 * N[(N[(k * z + N[(N[(a * t$95$1 + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision] / y0), $MachinePrecision]), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.6e-144], N[(-1.0 * N[(y3 * N[(N[(j * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.4e-33], N[(-1.0 * N[(z * N[(N[(t * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(i * N[(N[(c * t$95$1 + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -4.99999999999999973e48

   1. Initial program 24.6%

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

   2. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 51.2%

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

   if -4.99999999999999973e48 < y5 < -2.99999999999999989e-161

   1. Initial program 32.7%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 40.8%

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

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   7. Applied rewrites 45.3%

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

   if -2.99999999999999989e-161 < y5 < 4.6e-144

   1. Initial program 36.3%

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

   2. Taylor expanded in 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 36.9%

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

   if 4.6e-144 < y5 < 2.4e-33

   1. Initial program 34.0%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 38.3%

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

   if 2.4e-33 < y5

   1. Initial program 25.6%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 40.1%

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

Alternative 5: 40.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)\\ t_2 := y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_3 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y4 \leq -3 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq -1.1 \cdot 10^{-77}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot t\_3\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq -1.6 \cdot 10^{-286}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 2.7 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(y, a \cdot b - c \cdot i, y2 \cdot t\_3\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 1.15 \cdot 10^{+202}:\\ \;\;\;\;b \cdot \left(y \cdot \mathsf{fma}\left(-1, k \cdot y4, a \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* z (fma -1.0 (* y0 y3) (* i t)))))
        (t_2
         (*
          y4
          (-
           (fma b (- (* j t) (* k y)) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* t y2) (* y y3))))))
        (t_3 (- (* c y0) (* a y1))))
   (if (<= y4 -3e+18)
     t_2
     (if (<= y4 -1.1e-77)
       (*
        y2
        (-
         (fma k (- (* y1 y4) (* y0 y5)) (* x t_3))
         (* t (- (* c y4) (* a y5)))))
       (if (<= y4 -1.6e-286)
         t_1
         (if (<= y4 2.7e-56)
           (*
            x
            (-
             (fma y (- (* a b) (* c i)) (* y2 t_3))
             (* j (- (* b y0) (* i y1)))))
           (if (<= y4 6.5e+80)
             t_1
             (if (<= y4 1.15e+202)
               (* b (* y (fma -1.0 (* k y4) (* a x))))
               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 = c * (z * fma(-1.0, (y0 * y3), (i * t)));
	double t_2 = y4 * (fma(b, ((j * t) - (k * y)), (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	double t_3 = (c * y0) - (a * y1);
	double tmp;
	if (y4 <= -3e+18) {
		tmp = t_2;
	} else if (y4 <= -1.1e-77) {
		tmp = y2 * (fma(k, ((y1 * y4) - (y0 * y5)), (x * t_3)) - (t * ((c * y4) - (a * y5))));
	} else if (y4 <= -1.6e-286) {
		tmp = t_1;
	} else if (y4 <= 2.7e-56) {
		tmp = x * (fma(y, ((a * b) - (c * i)), (y2 * t_3)) - (j * ((b * y0) - (i * y1))));
	} else if (y4 <= 6.5e+80) {
		tmp = t_1;
	} else if (y4 <= 1.15e+202) {
		tmp = b * (y * fma(-1.0, (k * y4), (a * x)));
	} 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(c * Float64(z * fma(-1.0, Float64(y0 * y3), Float64(i * t))))
	t_2 = Float64(y4 * Float64(fma(b, Float64(Float64(j * t) - Float64(k * y)), Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y4 <= -3e+18)
		tmp = t_2;
	elseif (y4 <= -1.1e-77)
		tmp = Float64(y2 * Float64(fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(x * t_3)) - Float64(t * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (y4 <= -1.6e-286)
		tmp = t_1;
	elseif (y4 <= 2.7e-56)
		tmp = Float64(x * Float64(fma(y, Float64(Float64(a * b) - Float64(c * i)), Float64(y2 * t_3)) - Float64(j * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y4 <= 6.5e+80)
		tmp = t_1;
	elseif (y4 <= 1.15e+202)
		tmp = Float64(b * Float64(y * fma(-1.0, Float64(k * y4), Float64(a * x))));
	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[(c * N[(z * N[(-1.0 * N[(y0 * y3), $MachinePrecision] + N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -3e+18], t$95$2, If[LessEqual[y4, -1.1e-77], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.6e-286], t$95$1, If[LessEqual[y4, 2.7e-56], N[(x * N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.5e+80], t$95$1, If[LessEqual[y4, 1.15e+202], N[(b * N[(y * N[(-1.0 * N[(k * y4), $MachinePrecision] + N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -3e18 or 1.15e202 < y4

   1. Initial program 23.6%

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

   2. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 53.2%

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

   if -3e18 < y4 < -1.10000000000000003e-77

   1. Initial program 32.4%

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

   2. Taylor expanded in 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 40.7%

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

   if -1.10000000000000003e-77 < y4 < -1.60000000000000003e-286 or 2.69999999999999995e-56 < y4 < 6.4999999999999998e80

   1. Initial program 34.0%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 39.7%

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

   5. Taylor expanded in c around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 28.1

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

   7. Applied rewrites 28.1%

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

   if -1.60000000000000003e-286 < y4 < 2.69999999999999995e-56

   1. Initial program 36.0%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 39.4%

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

   if 6.4999999999999998e80 < y4 < 1.15e202

   1. Initial program 24.2%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 39.6%

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

   5. Taylor expanded in y around inf

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + \color{blue}{a \cdot x}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(y \cdot \mathsf{fma}\left(-1, k \cdot \color{blue}{y4}, a \cdot x\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(y \cdot \mathsf{fma}\left(-1, k \cdot y4, a \cdot x\right)\right) \]

      4. lower-*.f64 32.6

         \[\leadsto b \cdot \left(y \cdot \mathsf{fma}\left(-1, k \cdot y4, a \cdot x\right)\right) \]

   7. Applied rewrites 32.6%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1, k \cdot y4, a \cdot x\right)}\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 6: 40.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := c \cdot y4 - a \cdot y5\\ \mathbf{if}\;y3 \leq -1.22 \cdot 10^{-49}:\\ \;\;\;\;-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot t\_1\right) - y \cdot t\_2\right)\right)\\ \mathbf{elif}\;y3 \leq -3.35 \cdot 10^{-217}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(\mathsf{fma}\left(k, z, \frac{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y0}\right) - j \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq 1.42 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(y, a \cdot b - c \cdot i, y2 \cdot t\_1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 1.2 \cdot 10^{+168}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1))) (t_2 (- (* c y4) (* a y5))))
   (if (<= y3 -1.22e-49)
     (* -1.0 (* y3 (- (fma j (- (* y1 y4) (* y0 y5)) (* z t_1)) (* y t_2))))
     (if (<= y3 -3.35e-217)
       (*
        b
        (*
         y0
         (-
          (fma
           k
           z
           (/ (fma a (- (* x y) (* t z)) (* y4 (- (* j t) (* k y)))) y0))
          (* j x))))
       (if (<= y3 1.42e-40)
         (*
          x
          (-
           (fma y (- (* a b) (* c i)) (* y2 t_1))
           (* j (- (* b y0) (* i y1)))))
         (if (<= y3 1.2e+168)
           (* c (* z (fma -1.0 (* y0 y3) (* i t))))
           (* y (* y3 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 = (c * y0) - (a * y1);
	double t_2 = (c * y4) - (a * y5);
	double tmp;
	if (y3 <= -1.22e-49) {
		tmp = -1.0 * (y3 * (fma(j, ((y1 * y4) - (y0 * y5)), (z * t_1)) - (y * t_2)));
	} else if (y3 <= -3.35e-217) {
		tmp = b * (y0 * (fma(k, z, (fma(a, ((x * y) - (t * z)), (y4 * ((j * t) - (k * y)))) / y0)) - (j * x)));
	} else if (y3 <= 1.42e-40) {
		tmp = x * (fma(y, ((a * b) - (c * i)), (y2 * t_1)) - (j * ((b * y0) - (i * y1))));
	} else if (y3 <= 1.2e+168) {
		tmp = c * (z * fma(-1.0, (y0 * y3), (i * t)));
	} else {
		tmp = y * (y3 * 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(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(c * y4) - Float64(a * y5))
	tmp = 0.0
	if (y3 <= -1.22e-49)
		tmp = Float64(-1.0 * Float64(y3 * Float64(fma(j, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(z * t_1)) - Float64(y * t_2))));
	elseif (y3 <= -3.35e-217)
		tmp = Float64(b * Float64(y0 * Float64(fma(k, z, Float64(fma(a, Float64(Float64(x * y) - Float64(t * z)), Float64(y4 * Float64(Float64(j * t) - Float64(k * y)))) / y0)) - Float64(j * x))));
	elseif (y3 <= 1.42e-40)
		tmp = Float64(x * Float64(fma(y, Float64(Float64(a * b) - Float64(c * i)), Float64(y2 * t_1)) - Float64(j * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y3 <= 1.2e+168)
		tmp = Float64(c * Float64(z * fma(-1.0, Float64(y0 * y3), Float64(i * t))));
	else
		tmp = Float64(y * Float64(y3 * 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[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.22e-49], N[(-1.0 * N[(y3 * N[(N[(j * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -3.35e-217], N[(b * N[(y0 * N[(N[(k * z + N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y0), $MachinePrecision]), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.42e-40], N[(x * N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.2e+168], N[(c * N[(z * N[(-1.0 * N[(y0 * y3), $MachinePrecision] + N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(y3 * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -1.2199999999999999e-49

   1. Initial program 26.8%

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

   2. Taylor expanded in 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 45.6%

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

   if -1.2199999999999999e-49 < y3 < -3.35e-217

   1. Initial program 36.9%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.3%

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

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   7. Applied rewrites 40.8%

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

   if -3.35e-217 < y3 < 1.42000000000000001e-40

   1. Initial program 34.2%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 39.2%

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

   if 1.42000000000000001e-40 < y3 < 1.20000000000000005e168

   1. Initial program 29.0%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 39.1%

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

   5. Taylor expanded in c around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 27.6

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

   7. Applied rewrites 27.6%

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

   if 1.20000000000000005e168 < y3

   1. Initial program 20.9%

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

   2. Taylor expanded in 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 57.7%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - \color{blue}{a \cdot y5}\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot \color{blue}{y5}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lift-*.f64 44.7

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 7: 40.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (+
          (-
           (+
            (+
             (-
              (* (- (* 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))))))
   (if (<= t_1 INFINITY)
     t_1
     (*
      -1.0
      (*
       y3
       (-
        (fma j (- (* y1 y4) (* y0 y5)) (* z (- (* c y0) (* a y1))))
        (* y (- (* c y4) (* a 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 t_1 = (((((((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)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = -1.0 * (y3 * (fma(j, ((y1 * y4) - (y0 * y5)), (z * ((c * y0) - (a * y1)))) - (y * ((c * y4) - (a * y5)))));
	}
	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(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))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(-1.0 * Float64(y3 * Float64(fma(j, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(z * Float64(Float64(c * y0) - Float64(a * y1)))) - Float64(y * Float64(Float64(c * y4) - Float64(a * y5))))));
	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[(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]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(-1.0 * N[(y3 * N[(N[(j * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.7%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in 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 35.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 40.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot t - k \cdot y\\ t_2 := -1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, t\_1, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{if}\;y5 \leq -5 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq -3 \cdot 10^{-161}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(\mathsf{fma}\left(k, z, \frac{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot t\_1\right)}{y0}\right) - j \cdot x\right)\right)\\ \mathbf{elif}\;y5 \leq 3 \cdot 10^{+76}:\\ \;\;\;\;-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j t) (* k y)))
        (t_2
         (*
          -1.0
          (*
           y5
           (-
            (fma i t_1 (* y0 (- (* k y2) (* j y3))))
            (* a (- (* t y2) (* y y3))))))))
   (if (<= y5 -5e+48)
     t_2
     (if (<= y5 -3e-161)
       (*
        b
        (*
         y0
         (- (fma k z (/ (fma a (- (* x y) (* t z)) (* y4 t_1)) y0)) (* j x))))
       (if (<= y5 3e+76)
         (*
          -1.0
          (*
           y3
           (-
            (fma j (- (* y1 y4) (* y0 y5)) (* z (- (* c y0) (* a y1))))
            (* y (- (* c y4) (* a y5))))))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * t) - (k * y);
	double t_2 = -1.0 * (y5 * (fma(i, t_1, (y0 * ((k * y2) - (j * y3)))) - (a * ((t * y2) - (y * y3)))));
	double tmp;
	if (y5 <= -5e+48) {
		tmp = t_2;
	} else if (y5 <= -3e-161) {
		tmp = b * (y0 * (fma(k, z, (fma(a, ((x * y) - (t * z)), (y4 * t_1)) / y0)) - (j * x)));
	} else if (y5 <= 3e+76) {
		tmp = -1.0 * (y3 * (fma(j, ((y1 * y4) - (y0 * y5)), (z * ((c * y0) - (a * y1)))) - (y * ((c * y4) - (a * y5)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * t) - Float64(k * y))
	t_2 = Float64(-1.0 * Float64(y5 * Float64(fma(i, t_1, Float64(y0 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(a * Float64(Float64(t * y2) - Float64(y * y3))))))
	tmp = 0.0
	if (y5 <= -5e+48)
		tmp = t_2;
	elseif (y5 <= -3e-161)
		tmp = Float64(b * Float64(y0 * Float64(fma(k, z, Float64(fma(a, Float64(Float64(x * y) - Float64(t * z)), Float64(y4 * t_1)) / y0)) - Float64(j * x))));
	elseif (y5 <= 3e+76)
		tmp = Float64(-1.0 * Float64(y3 * Float64(fma(j, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(z * Float64(Float64(c * y0) - Float64(a * y1)))) - Float64(y * Float64(Float64(c * y4) - Float64(a * y5))))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 * N[(y5 * N[(N[(i * t$95$1 + N[(y0 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -5e+48], t$95$2, If[LessEqual[y5, -3e-161], N[(b * N[(y0 * N[(N[(k * z + N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] / y0), $MachinePrecision]), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3e+76], N[(-1.0 * N[(y3 * N[(N[(j * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -4.99999999999999973e48 or 2.9999999999999998e76 < y5

   1. Initial program 24.2%

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

   2. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 52.5%

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

   if -4.99999999999999973e48 < y5 < -2.99999999999999989e-161

   1. Initial program 32.7%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 40.8%

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

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   7. Applied rewrites 45.3%

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

   if -2.99999999999999989e-161 < y5 < 2.9999999999999998e76

   1. Initial program 34.3%

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

   2. Taylor expanded in 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 36.8%

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

Alternative 9: 39.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y4 - a \cdot y5\\ t_2 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y3 \leq -5.8 \cdot 10^{+149}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;y3 \leq -1.52 \cdot 10^{+22}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot t\_2\right) - t \cdot t\_1\right)\\ \mathbf{elif}\;y3 \leq -5.4 \cdot 10^{-156}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \mathbf{elif}\;y3 \leq 1.42 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(y, a \cdot b - c \cdot i, y2 \cdot t\_2\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 1.2 \cdot 10^{+168}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y4) (* a y5))) (t_2 (- (* c y0) (* a y1))))
   (if (<= y3 -5.8e+149)
     (* y3 (* y5 (- (* j y0) (* a y))))
     (if (<= y3 -1.52e+22)
       (* y2 (- (fma k (- (* y1 y4) (* y0 y5)) (* x t_2)) (* t t_1)))
       (if (<= y3 -5.4e-156)
         (*
          b
          (-
           (fma a (- (* x y) (* t z)) (* y4 (- (* j t) (* k y))))
           (* y0 (- (* j x) (* k z)))))
         (if (<= y3 1.42e-40)
           (*
            x
            (-
             (fma y (- (* a b) (* c i)) (* y2 t_2))
             (* j (- (* b y0) (* i y1)))))
           (if (<= y3 1.2e+168)
             (* c (* z (fma -1.0 (* y0 y3) (* i t))))
             (* y (* y3 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 = (c * y4) - (a * y5);
	double t_2 = (c * y0) - (a * y1);
	double tmp;
	if (y3 <= -5.8e+149) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (y3 <= -1.52e+22) {
		tmp = y2 * (fma(k, ((y1 * y4) - (y0 * y5)), (x * t_2)) - (t * t_1));
	} else if (y3 <= -5.4e-156) {
		tmp = b * (fma(a, ((x * y) - (t * z)), (y4 * ((j * t) - (k * y)))) - (y0 * ((j * x) - (k * z))));
	} else if (y3 <= 1.42e-40) {
		tmp = x * (fma(y, ((a * b) - (c * i)), (y2 * t_2)) - (j * ((b * y0) - (i * y1))));
	} else if (y3 <= 1.2e+168) {
		tmp = c * (z * fma(-1.0, (y0 * y3), (i * t)));
	} else {
		tmp = y * (y3 * 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(c * y4) - Float64(a * y5))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y3 <= -5.8e+149)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (y3 <= -1.52e+22)
		tmp = Float64(y2 * Float64(fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(x * t_2)) - Float64(t * t_1)));
	elseif (y3 <= -5.4e-156)
		tmp = Float64(b * Float64(fma(a, Float64(Float64(x * y) - Float64(t * z)), Float64(y4 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(y0 * Float64(Float64(j * x) - Float64(k * z)))));
	elseif (y3 <= 1.42e-40)
		tmp = Float64(x * Float64(fma(y, Float64(Float64(a * b) - Float64(c * i)), Float64(y2 * t_2)) - Float64(j * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y3 <= 1.2e+168)
		tmp = Float64(c * Float64(z * fma(-1.0, Float64(y0 * y3), Float64(i * t))));
	else
		tmp = Float64(y * Float64(y3 * 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[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -5.8e+149], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.52e+22], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -5.4e-156], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.42e-40], N[(x * N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.2e+168], N[(c * N[(z * N[(-1.0 * N[(y0 * y3), $MachinePrecision] + N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y3 < -5.8000000000000004e149

   1. Initial program 21.7%

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

   2. Taylor expanded in 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 57.9%

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

   5. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 39.8

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 39.8%

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

   if -5.8000000000000004e149 < y3 < -1.52e22

   1. Initial program 30.2%

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

   2. Taylor expanded in 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 35.7%

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

   if -1.52e22 < y3 < -5.40000000000000024e-156

   1. Initial program 33.9%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.8%

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

   if -5.40000000000000024e-156 < y3 < 1.42000000000000001e-40

   1. Initial program 35.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 39.5%

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

   if 1.42000000000000001e-40 < y3 < 1.20000000000000005e168

   1. Initial program 29.0%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 39.1%

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

   5. Taylor expanded in c around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 27.6

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

   7. Applied rewrites 27.6%

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

   if 1.20000000000000005e168 < y3

   1. Initial program 20.9%

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

   2. Taylor expanded in 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 57.7%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - \color{blue}{a \cdot y5}\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot \color{blue}{y5}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lift-*.f64 44.7

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 10: 37.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.42 \cdot 10^{+156}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(\mathsf{fma}\left(k, z, \frac{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y0}\right) - j \cdot x\right)\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+231}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.42e+156)
   (* y3 (* y5 (- (* j y0) (* a y))))
   (if (<= j 2.9e+122)
     (*
      b
      (*
       y0
       (-
        (fma k z (/ (fma a (- (* x y) (* t z)) (* y4 (- (* j t) (* k y)))) y0))
        (* j x))))
     (if (<= j 2.9e+231)
       (* y4 (* -1.0 (* y3 (* y (- (/ (* j y1) y) c)))))
       (* b (* y0 (* j (- (/ (* t y4) y0) x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.42e+156) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= 2.9e+122) {
		tmp = b * (y0 * (fma(k, z, (fma(a, ((x * y) - (t * z)), (y4 * ((j * t) - (k * y)))) / y0)) - (j * x)));
	} else if (j <= 2.9e+231) {
		tmp = y4 * (-1.0 * (y3 * (y * (((j * y1) / y) - c))));
	} else {
		tmp = b * (y0 * (j * (((t * y4) / y0) - x)));
	}
	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 <= -1.42e+156)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (j <= 2.9e+122)
		tmp = Float64(b * Float64(y0 * Float64(fma(k, z, Float64(fma(a, Float64(Float64(x * y) - Float64(t * z)), Float64(y4 * Float64(Float64(j * t) - Float64(k * y)))) / y0)) - Float64(j * x))));
	elseif (j <= 2.9e+231)
		tmp = Float64(y4 * Float64(-1.0 * Float64(y3 * Float64(y * Float64(Float64(Float64(j * y1) / y) - c)))));
	else
		tmp = Float64(b * Float64(y0 * Float64(j * Float64(Float64(Float64(t * y4) / y0) - x))));
	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, -1.42e+156], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.9e+122], N[(b * N[(y0 * N[(N[(k * z + N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y0), $MachinePrecision]), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.9e+231], N[(y4 * N[(-1.0 * N[(y3 * N[(y * N[(N[(N[(j * y1), $MachinePrecision] / y), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y0 * N[(j * N[(N[(N[(t * y4), $MachinePrecision] / y0), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.41999999999999998e156

   1. Initial program 22.0%

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

   2. Taylor expanded in 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 43.1%

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

   5. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 35.5

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 35.5%

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

   if -1.41999999999999998e156 < j < 2.9000000000000001e122

   1. Initial program 32.9%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.3%

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

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   7. Applied rewrites 41.2%

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

   if 2.9000000000000001e122 < j < 2.9000000000000001e231

   1. Initial program 25.2%

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

   2. Taylor expanded in 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 37.8%

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

   5. Taylor expanded in y3 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 33.9

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 33.9%

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

   8. Taylor expanded in y around inf

      \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - \color{blue}{c}\right)\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      4. lift-*.f64 38.0

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

   10. Applied rewrites 38.0%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - \color{blue}{c}\right)\right)\right)\right) \]

   if 2.9000000000000001e231 < j

   1. Initial program 21.2%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 35.6%

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

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   7. Applied rewrites 38.6%

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

   8. Taylor expanded in j around inf

      \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - \color{blue}{x}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      4. lower-*.f64 51.5

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

   10. Applied rewrites 51.5%

       \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - \color{blue}{x}\right)\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 36.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.2 \cdot 10^{+60}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-190}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 2.55 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(y, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+231}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.2e+60)
   (* y3 (* y5 (- (* j y0) (* a y))))
   (if (<= j 7.5e-190)
     (*
      b
      (-
       (fma a (- (* x y) (* t z)) (* y4 (- (* j t) (* k y))))
       (* y0 (- (* j x) (* k z)))))
     (if (<= j 8.8e-85)
       (* a (* z (fma -1.0 (* b t) (* y1 y3))))
       (if (<= j 2.55e+119)
         (*
          x
          (-
           (fma y (- (* a b) (* c i)) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* b y0) (* i y1)))))
         (if (<= j 2.9e+231)
           (* y4 (* -1.0 (* y3 (* y (- (/ (* j y1) y) c)))))
           (* b (* y0 (* j (- (/ (* t y4) y0) x))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.2e+60) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= 7.5e-190) {
		tmp = b * (fma(a, ((x * y) - (t * z)), (y4 * ((j * t) - (k * y)))) - (y0 * ((j * x) - (k * z))));
	} else if (j <= 8.8e-85) {
		tmp = a * (z * fma(-1.0, (b * t), (y1 * y3)));
	} else if (j <= 2.55e+119) {
		tmp = x * (fma(y, ((a * b) - (c * i)), (y2 * ((c * y0) - (a * y1)))) - (j * ((b * y0) - (i * y1))));
	} else if (j <= 2.9e+231) {
		tmp = y4 * (-1.0 * (y3 * (y * (((j * y1) / y) - c))));
	} else {
		tmp = b * (y0 * (j * (((t * y4) / y0) - x)));
	}
	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 <= -1.2e+60)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (j <= 7.5e-190)
		tmp = Float64(b * Float64(fma(a, Float64(Float64(x * y) - Float64(t * z)), Float64(y4 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(y0 * Float64(Float64(j * x) - Float64(k * z)))));
	elseif (j <= 8.8e-85)
		tmp = Float64(a * Float64(z * fma(-1.0, Float64(b * t), Float64(y1 * y3))));
	elseif (j <= 2.55e+119)
		tmp = Float64(x * Float64(fma(y, Float64(Float64(a * b) - Float64(c * i)), Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) - Float64(j * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (j <= 2.9e+231)
		tmp = Float64(y4 * Float64(-1.0 * Float64(y3 * Float64(y * Float64(Float64(Float64(j * y1) / y) - c)))));
	else
		tmp = Float64(b * Float64(y0 * Float64(j * Float64(Float64(Float64(t * y4) / y0) - x))));
	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, -1.2e+60], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e-190], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.8e-85], N[(a * N[(z * N[(-1.0 * N[(b * t), $MachinePrecision] + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.55e+119], N[(x * N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.9e+231], N[(y4 * N[(-1.0 * N[(y3 * N[(y * N[(N[(N[(j * y1), $MachinePrecision] / y), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y0 * N[(j * N[(N[(N[(t * y4), $MachinePrecision] / y0), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.2e60

   1. Initial program 24.1%

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

   2. Taylor expanded in 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 41.9%

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

   5. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 33.6

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 33.6%

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

   if -1.2e60 < j < 7.5e-190

   1. Initial program 34.0%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.3%

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

   if 7.5e-190 < j < 8.8e-85

   1. Initial program 35.8%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 42.0%

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

   5. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 30.1

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

   7. Applied rewrites 30.1%

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

   if 8.8e-85 < j < 2.54999999999999992e119

   1. Initial program 31.3%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.5%

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

   if 2.54999999999999992e119 < j < 2.9000000000000001e231

   1. Initial program 25.3%

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

   2. Taylor expanded in 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 37.9%

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

   5. Taylor expanded in y3 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 33.7

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 33.7%

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

   8. Taylor expanded in y around inf

      \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - \color{blue}{c}\right)\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      4. lift-*.f64 37.7

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

   10. Applied rewrites 37.7%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - \color{blue}{c}\right)\right)\right)\right) \]

   if 2.9000000000000001e231 < j

   1. Initial program 21.2%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 35.6%

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

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   7. Applied rewrites 38.6%

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

   8. Taylor expanded in j around inf

      \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - \color{blue}{x}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      4. lower-*.f64 51.5

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

   10. Applied rewrites 51.5%

       \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - \color{blue}{x}\right)\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 12: 35.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.2 \cdot 10^{+147}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-121}:\\ \;\;\;\;-1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-303}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot \left(y4 + -1 \cdot \frac{y0 \cdot y5}{y1}\right)\right)\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-190}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + -1 \cdot \frac{y \cdot y5}{y1}\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+231}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -6.2e+147)
   (* y3 (* y5 (- (* j y0) (* a y))))
   (if (<= j -3.6e-121)
     (* -1.0 (* y (* y4 (- (* b k) (* c y3)))))
     (if (<= j -6e-303)
       (* k (* y2 (* y1 (+ y4 (* -1.0 (/ (* y0 y5) y1))))))
       (if (<= j 7.8e-190)
         (* k (* z (- (* b y0) (* i y1))))
         (if (<= j 3.2e+65)
           (* a (* y3 (* y1 (+ z (* -1.0 (/ (* y y5) y1))))))
           (if (<= j 2.9e+231)
             (* y4 (* -1.0 (* y3 (* y (- (/ (* j y1) y) c)))))
             (* b (* y0 (* j (- (/ (* t y4) y0) x)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -6.2e+147) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= -3.6e-121) {
		tmp = -1.0 * (y * (y4 * ((b * k) - (c * y3))));
	} else if (j <= -6e-303) {
		tmp = k * (y2 * (y1 * (y4 + (-1.0 * ((y0 * y5) / y1)))));
	} else if (j <= 7.8e-190) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (j <= 3.2e+65) {
		tmp = a * (y3 * (y1 * (z + (-1.0 * ((y * y5) / y1)))));
	} else if (j <= 2.9e+231) {
		tmp = y4 * (-1.0 * (y3 * (y * (((j * y1) / y) - c))));
	} else {
		tmp = b * (y0 * (j * (((t * y4) / y0) - x)));
	}
	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 (j <= (-6.2d+147)) then
        tmp = y3 * (y5 * ((j * y0) - (a * y)))
    else if (j <= (-3.6d-121)) then
        tmp = (-1.0d0) * (y * (y4 * ((b * k) - (c * y3))))
    else if (j <= (-6d-303)) then
        tmp = k * (y2 * (y1 * (y4 + ((-1.0d0) * ((y0 * y5) / y1)))))
    else if (j <= 7.8d-190) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (j <= 3.2d+65) then
        tmp = a * (y3 * (y1 * (z + ((-1.0d0) * ((y * y5) / y1)))))
    else if (j <= 2.9d+231) then
        tmp = y4 * ((-1.0d0) * (y3 * (y * (((j * y1) / y) - c))))
    else
        tmp = b * (y0 * (j * (((t * y4) / y0) - x)))
    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 (j <= -6.2e+147) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= -3.6e-121) {
		tmp = -1.0 * (y * (y4 * ((b * k) - (c * y3))));
	} else if (j <= -6e-303) {
		tmp = k * (y2 * (y1 * (y4 + (-1.0 * ((y0 * y5) / y1)))));
	} else if (j <= 7.8e-190) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (j <= 3.2e+65) {
		tmp = a * (y3 * (y1 * (z + (-1.0 * ((y * y5) / y1)))));
	} else if (j <= 2.9e+231) {
		tmp = y4 * (-1.0 * (y3 * (y * (((j * y1) / y) - c))));
	} else {
		tmp = b * (y0 * (j * (((t * y4) / y0) - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -6.2e+147:
		tmp = y3 * (y5 * ((j * y0) - (a * y)))
	elif j <= -3.6e-121:
		tmp = -1.0 * (y * (y4 * ((b * k) - (c * y3))))
	elif j <= -6e-303:
		tmp = k * (y2 * (y1 * (y4 + (-1.0 * ((y0 * y5) / y1)))))
	elif j <= 7.8e-190:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif j <= 3.2e+65:
		tmp = a * (y3 * (y1 * (z + (-1.0 * ((y * y5) / y1)))))
	elif j <= 2.9e+231:
		tmp = y4 * (-1.0 * (y3 * (y * (((j * y1) / y) - c))))
	else:
		tmp = b * (y0 * (j * (((t * y4) / y0) - x)))
	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 <= -6.2e+147)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (j <= -3.6e-121)
		tmp = Float64(-1.0 * Float64(y * Float64(y4 * Float64(Float64(b * k) - Float64(c * y3)))));
	elseif (j <= -6e-303)
		tmp = Float64(k * Float64(y2 * Float64(y1 * Float64(y4 + Float64(-1.0 * Float64(Float64(y0 * y5) / y1))))));
	elseif (j <= 7.8e-190)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (j <= 3.2e+65)
		tmp = Float64(a * Float64(y3 * Float64(y1 * Float64(z + Float64(-1.0 * Float64(Float64(y * y5) / y1))))));
	elseif (j <= 2.9e+231)
		tmp = Float64(y4 * Float64(-1.0 * Float64(y3 * Float64(y * Float64(Float64(Float64(j * y1) / y) - c)))));
	else
		tmp = Float64(b * Float64(y0 * Float64(j * Float64(Float64(Float64(t * y4) / y0) - x))));
	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 (j <= -6.2e+147)
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	elseif (j <= -3.6e-121)
		tmp = -1.0 * (y * (y4 * ((b * k) - (c * y3))));
	elseif (j <= -6e-303)
		tmp = k * (y2 * (y1 * (y4 + (-1.0 * ((y0 * y5) / y1)))));
	elseif (j <= 7.8e-190)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (j <= 3.2e+65)
		tmp = a * (y3 * (y1 * (z + (-1.0 * ((y * y5) / y1)))));
	elseif (j <= 2.9e+231)
		tmp = y4 * (-1.0 * (y3 * (y * (((j * y1) / y) - c))));
	else
		tmp = b * (y0 * (j * (((t * y4) / y0) - x)));
	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[j, -6.2e+147], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.6e-121], N[(-1.0 * N[(y * N[(y4 * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6e-303], N[(k * N[(y2 * N[(y1 * N[(y4 + N[(-1.0 * N[(N[(y0 * y5), $MachinePrecision] / y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.8e-190], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e+65], N[(a * N[(y3 * N[(y1 * N[(z + N[(-1.0 * N[(N[(y * y5), $MachinePrecision] / y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.9e+231], N[(y4 * N[(-1.0 * N[(y3 * N[(y * N[(N[(N[(j * y1), $MachinePrecision] / y), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y0 * N[(j * N[(N[(N[(t * y4), $MachinePrecision] / y0), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -6.2000000000000001e147

   1. Initial program 22.2%

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

   2. Taylor expanded in 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 42.6%

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

   5. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 35.3

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 35.3%

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

   if -6.2000000000000001e147 < j < -3.59999999999999984e-121

   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 38.1%

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

   5. Taylor expanded in y around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \color{blue}{\left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \color{blue}{\left(b \cdot k - c \cdot y3\right)}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - \color{blue}{c \cdot y3}\right)\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot \color{blue}{y3}\right)\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right) \]

      6. lower-*.f64 27.3

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right) \]

   7. Applied rewrites 27.3%

      \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right)} \]

   if -3.59999999999999984e-121 < j < -6.00000000000000055e-303

   1. Initial program 35.8%

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

   2. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 39.5%

      \[\leadsto \color{blue}{k \cdot \left(\mathsf{fma}\left(-1, y \cdot \left(b \cdot y4 - i \cdot y5\right), y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y2 around inf

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

      4. lift-*.f64 27.4

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

   7. Applied rewrites 27.4%

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

   8. Taylor expanded in y1 around inf

      \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot \left(y4 + \color{blue}{-1 \cdot \frac{y0 \cdot y5}{y1}}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot \left(y4 + -1 \cdot \frac{y0 \cdot y5}{y1}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot \left(y4 + -1 \cdot \frac{y0 \cdot y5}{y1}\right)\right)\right) \]

      5. lift-*.f64 29.6

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot \left(y4 + -1 \cdot \frac{y0 \cdot y5}{y1}\right)\right)\right) \]

   10. Applied rewrites 29.6%

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

   if -6.00000000000000055e-303 < j < 7.7999999999999999e-190

   1. Initial program 35.2%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 40.8%

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

   5. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 28.3

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

   7. Applied rewrites 28.3%

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

   8. Taylor expanded in k around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      5. lower-*.f64 26.9

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   10. Applied rewrites 26.9%

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

   if 7.7999999999999999e-190 < j < 3.20000000000000007e65

   1. Initial program 33.0%

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

   2. Taylor expanded in 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 33.0%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

      5. lower-*.f64 26.2

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   8. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + \color{blue}{-1 \cdot \frac{y \cdot y5}{y1}}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + -1 \cdot \frac{y \cdot y5}{y1}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + -1 \cdot \frac{y \cdot y5}{y1}\right)\right)\right) \]

      5. lift-*.f64 28.6

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + -1 \cdot \frac{y \cdot y5}{y1}\right)\right)\right) \]

   10. Applied rewrites 28.6%

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

   if 3.20000000000000007e65 < j < 2.9000000000000001e231

   1. Initial program 27.4%

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

   2. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y3 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 31.5

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 31.5%

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

   8. Taylor expanded in y around inf

      \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - \color{blue}{c}\right)\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      4. lift-*.f64 35.6

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

   10. Applied rewrites 35.6%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - \color{blue}{c}\right)\right)\right)\right) \]

   if 2.9000000000000001e231 < j

   1. Initial program 21.2%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 35.6%

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

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   7. Applied rewrites 38.6%

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

   8. Taylor expanded in j around inf

      \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - \color{blue}{x}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      4. lower-*.f64 51.5

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

   10. Applied rewrites 51.5%

       \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - \color{blue}{x}\right)\right)\right) \]
3. Recombined 7 regimes into one program.
4. Add Preprocessing

Alternative 13: 32.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.2 \cdot 10^{+147}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-121}:\\ \;\;\;\;-1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-303}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-190}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + -1 \cdot \frac{y \cdot y5}{y1}\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+231}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -6.2e+147)
   (* y3 (* y5 (- (* j y0) (* a y))))
   (if (<= j -3.6e-121)
     (* -1.0 (* y (* y4 (- (* b k) (* c y3)))))
     (if (<= j -6e-303)
       (* k (* y2 (- (* y1 y4) (* y0 y5))))
       (if (<= j 7.8e-190)
         (* k (* z (- (* b y0) (* i y1))))
         (if (<= j 3.2e+65)
           (* a (* y3 (* y1 (+ z (* -1.0 (/ (* y y5) y1))))))
           (if (<= j 2.9e+231)
             (* y4 (* -1.0 (* y3 (* y (- (/ (* j y1) y) c)))))
             (* b (* y0 (* j (- (/ (* t y4) y0) x)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -6.2e+147) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= -3.6e-121) {
		tmp = -1.0 * (y * (y4 * ((b * k) - (c * y3))));
	} else if (j <= -6e-303) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (j <= 7.8e-190) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (j <= 3.2e+65) {
		tmp = a * (y3 * (y1 * (z + (-1.0 * ((y * y5) / y1)))));
	} else if (j <= 2.9e+231) {
		tmp = y4 * (-1.0 * (y3 * (y * (((j * y1) / y) - c))));
	} else {
		tmp = b * (y0 * (j * (((t * y4) / y0) - x)));
	}
	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 (j <= (-6.2d+147)) then
        tmp = y3 * (y5 * ((j * y0) - (a * y)))
    else if (j <= (-3.6d-121)) then
        tmp = (-1.0d0) * (y * (y4 * ((b * k) - (c * y3))))
    else if (j <= (-6d-303)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (j <= 7.8d-190) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (j <= 3.2d+65) then
        tmp = a * (y3 * (y1 * (z + ((-1.0d0) * ((y * y5) / y1)))))
    else if (j <= 2.9d+231) then
        tmp = y4 * ((-1.0d0) * (y3 * (y * (((j * y1) / y) - c))))
    else
        tmp = b * (y0 * (j * (((t * y4) / y0) - x)))
    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 (j <= -6.2e+147) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= -3.6e-121) {
		tmp = -1.0 * (y * (y4 * ((b * k) - (c * y3))));
	} else if (j <= -6e-303) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (j <= 7.8e-190) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (j <= 3.2e+65) {
		tmp = a * (y3 * (y1 * (z + (-1.0 * ((y * y5) / y1)))));
	} else if (j <= 2.9e+231) {
		tmp = y4 * (-1.0 * (y3 * (y * (((j * y1) / y) - c))));
	} else {
		tmp = b * (y0 * (j * (((t * y4) / y0) - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -6.2e+147:
		tmp = y3 * (y5 * ((j * y0) - (a * y)))
	elif j <= -3.6e-121:
		tmp = -1.0 * (y * (y4 * ((b * k) - (c * y3))))
	elif j <= -6e-303:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif j <= 7.8e-190:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif j <= 3.2e+65:
		tmp = a * (y3 * (y1 * (z + (-1.0 * ((y * y5) / y1)))))
	elif j <= 2.9e+231:
		tmp = y4 * (-1.0 * (y3 * (y * (((j * y1) / y) - c))))
	else:
		tmp = b * (y0 * (j * (((t * y4) / y0) - x)))
	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 <= -6.2e+147)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (j <= -3.6e-121)
		tmp = Float64(-1.0 * Float64(y * Float64(y4 * Float64(Float64(b * k) - Float64(c * y3)))));
	elseif (j <= -6e-303)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (j <= 7.8e-190)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (j <= 3.2e+65)
		tmp = Float64(a * Float64(y3 * Float64(y1 * Float64(z + Float64(-1.0 * Float64(Float64(y * y5) / y1))))));
	elseif (j <= 2.9e+231)
		tmp = Float64(y4 * Float64(-1.0 * Float64(y3 * Float64(y * Float64(Float64(Float64(j * y1) / y) - c)))));
	else
		tmp = Float64(b * Float64(y0 * Float64(j * Float64(Float64(Float64(t * y4) / y0) - x))));
	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 (j <= -6.2e+147)
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	elseif (j <= -3.6e-121)
		tmp = -1.0 * (y * (y4 * ((b * k) - (c * y3))));
	elseif (j <= -6e-303)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (j <= 7.8e-190)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (j <= 3.2e+65)
		tmp = a * (y3 * (y1 * (z + (-1.0 * ((y * y5) / y1)))));
	elseif (j <= 2.9e+231)
		tmp = y4 * (-1.0 * (y3 * (y * (((j * y1) / y) - c))));
	else
		tmp = b * (y0 * (j * (((t * y4) / y0) - x)));
	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[j, -6.2e+147], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.6e-121], N[(-1.0 * N[(y * N[(y4 * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6e-303], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.8e-190], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e+65], N[(a * N[(y3 * N[(y1 * N[(z + N[(-1.0 * N[(N[(y * y5), $MachinePrecision] / y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.9e+231], N[(y4 * N[(-1.0 * N[(y3 * N[(y * N[(N[(N[(j * y1), $MachinePrecision] / y), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y0 * N[(j * N[(N[(N[(t * y4), $MachinePrecision] / y0), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -6.2000000000000001e147

   1. Initial program 22.2%

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

   2. Taylor expanded in 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 42.6%

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

   5. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 35.3

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 35.3%

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

   if -6.2000000000000001e147 < j < -3.59999999999999984e-121

   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 38.1%

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

   5. Taylor expanded in y around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \color{blue}{\left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \color{blue}{\left(b \cdot k - c \cdot y3\right)}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - \color{blue}{c \cdot y3}\right)\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot \color{blue}{y3}\right)\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right) \]

      6. lower-*.f64 27.3

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right) \]

   7. Applied rewrites 27.3%

      \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right)} \]

   if -3.59999999999999984e-121 < j < -6.00000000000000055e-303

   1. Initial program 35.8%

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

   2. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 39.5%

      \[\leadsto \color{blue}{k \cdot \left(\mathsf{fma}\left(-1, y \cdot \left(b \cdot y4 - i \cdot y5\right), y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y2 around inf

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

      4. lift-*.f64 27.4

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

   7. Applied rewrites 27.4%

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

   if -6.00000000000000055e-303 < j < 7.7999999999999999e-190

   1. Initial program 35.2%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 40.8%

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

   5. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 28.3

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

   7. Applied rewrites 28.3%

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

   8. Taylor expanded in k around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      5. lower-*.f64 26.9

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   10. Applied rewrites 26.9%

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

   if 7.7999999999999999e-190 < j < 3.20000000000000007e65

   1. Initial program 33.0%

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

   2. Taylor expanded in 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 33.0%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

      5. lower-*.f64 26.2

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   8. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + \color{blue}{-1 \cdot \frac{y \cdot y5}{y1}}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + -1 \cdot \frac{y \cdot y5}{y1}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + -1 \cdot \frac{y \cdot y5}{y1}\right)\right)\right) \]

      5. lift-*.f64 28.6

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + -1 \cdot \frac{y \cdot y5}{y1}\right)\right)\right) \]

   10. Applied rewrites 28.6%

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

   if 3.20000000000000007e65 < j < 2.9000000000000001e231

   1. Initial program 27.4%

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

   2. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y3 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 31.5

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 31.5%

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

   8. Taylor expanded in y around inf

      \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - \color{blue}{c}\right)\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      4. lift-*.f64 35.6

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

   10. Applied rewrites 35.6%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - \color{blue}{c}\right)\right)\right)\right) \]

   if 2.9000000000000001e231 < j

   1. Initial program 21.2%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 35.6%

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

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   7. Applied rewrites 38.6%

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

   8. Taylor expanded in j around inf

      \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - \color{blue}{x}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      4. lower-*.f64 51.5

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

   10. Applied rewrites 51.5%

       \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - \color{blue}{x}\right)\right)\right) \]
3. Recombined 7 regimes into one program.
4. Add Preprocessing

Alternative 14: 32.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)\\ \mathbf{if}\;y4 \leq -1.62 \cdot 10^{+193}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -1.1 \cdot 10^{+101}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{elif}\;y4 \leq -5.4 \cdot 10^{+29}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -3 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 2.7 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 3 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* z (fma -1.0 (* y0 y3) (* i t))))))
   (if (<= y4 -1.62e+193)
     (* y1 (* y4 (- (* k y2) (* j y3))))
     (if (<= y4 -1.1e+101)
       (* c (* y0 (- (* x y2) (* y3 z))))
       (if (<= y4 -5.4e+29)
         (* y4 (* -1.0 (* y3 (- (* j y1) (* c y)))))
         (if (<= y4 -3e-287)
           t_1
           (if (<= y4 2.7e-56)
             (* b (* x (- (* a y) (* j y0))))
             (if (<= y4 3e+98)
               t_1
               (* -1.0 (* y (* y4 (- (* b k) (* c y3)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (z * fma(-1.0, (y0 * y3), (i * t)));
	double tmp;
	if (y4 <= -1.62e+193) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (y4 <= -1.1e+101) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else if (y4 <= -5.4e+29) {
		tmp = y4 * (-1.0 * (y3 * ((j * y1) - (c * y))));
	} else if (y4 <= -3e-287) {
		tmp = t_1;
	} else if (y4 <= 2.7e-56) {
		tmp = b * (x * ((a * y) - (j * y0)));
	} else if (y4 <= 3e+98) {
		tmp = t_1;
	} else {
		tmp = -1.0 * (y * (y4 * ((b * k) - (c * y3))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(z * fma(-1.0, Float64(y0 * y3), Float64(i * t))))
	tmp = 0.0
	if (y4 <= -1.62e+193)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y4 <= -1.1e+101)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	elseif (y4 <= -5.4e+29)
		tmp = Float64(y4 * Float64(-1.0 * Float64(y3 * Float64(Float64(j * y1) - Float64(c * y)))));
	elseif (y4 <= -3e-287)
		tmp = t_1;
	elseif (y4 <= 2.7e-56)
		tmp = Float64(b * Float64(x * Float64(Float64(a * y) - Float64(j * y0))));
	elseif (y4 <= 3e+98)
		tmp = t_1;
	else
		tmp = Float64(-1.0 * Float64(y * Float64(y4 * Float64(Float64(b * k) - Float64(c * y3)))));
	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[(c * N[(z * N[(-1.0 * N[(y0 * y3), $MachinePrecision] + N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.62e+193], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.1e+101], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -5.4e+29], N[(y4 * N[(-1.0 * N[(y3 * N[(N[(j * y1), $MachinePrecision] - N[(c * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -3e-287], t$95$1, If[LessEqual[y4, 2.7e-56], N[(b * N[(x * N[(N[(a * y), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3e+98], t$95$1, N[(-1.0 * N[(y * N[(y4 * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -1.62000000000000004e193

   1. Initial program 20.1%

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

   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 59.5%

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

   5. Taylor expanded in y3 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 41.2

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 41.2%

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

   8. Taylor expanded in y1 around inf

      \[\leadsto y1 \cdot \color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

      5. lower-*.f64 48.4

         \[\leadsto y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   10. Applied rewrites 48.4%

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

   if -1.62000000000000004e193 < y4 < -1.1e101

   1. Initial program 27.4%

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

   2. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 32.9%

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

   5. Taylor expanded in c around inf

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. 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. lift--.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      5. lift-*.f64 26.6

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   7. Applied rewrites 26.6%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -1.1e101 < y4 < -5.4e29

   1. Initial program 28.7%

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

   2. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 38.2%

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

   5. Taylor expanded in y3 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 26.2

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 26.2%

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

   if -5.4e29 < y4 < -2.99999999999999992e-287 or 2.69999999999999995e-56 < y4 < 3.0000000000000001e98

   1. Initial program 33.6%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 38.9%

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

   5. Taylor expanded in c around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 27.2

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

   7. Applied rewrites 27.2%

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

   if -2.99999999999999992e-287 < y4 < 2.69999999999999995e-56

   1. Initial program 35.9%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 32.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 26.0

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

   7. Applied rewrites 26.0%

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

   if 3.0000000000000001e98 < y4

   1. Initial program 21.2%

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

   2. Taylor expanded in 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 53.8%

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

   5. Taylor expanded in y around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \color{blue}{\left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \color{blue}{\left(b \cdot k - c \cdot y3\right)}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - \color{blue}{c \cdot y3}\right)\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot \color{blue}{y3}\right)\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right) \]

      6. lower-*.f64 42.7

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right) \]

   7. Applied rewrites 42.7%

      \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right)} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 15: 31.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.2 \cdot 10^{+60}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-196}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + -1 \cdot \frac{y \cdot y5}{y1}\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+231}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.2e+60)
   (* y3 (* y5 (- (* j y0) (* a y))))
   (if (<= j 8e-196)
     (*
      b
      (-
       (fma a (- (* x y) (* t z)) (* y4 (- (* j t) (* k y))))
       (* y0 (- (* j x) (* k z)))))
     (if (<= j 3.2e+65)
       (* a (* y3 (* y1 (+ z (* -1.0 (/ (* y y5) y1))))))
       (if (<= j 2.9e+231)
         (* y4 (* -1.0 (* y3 (* y (- (/ (* j y1) y) c)))))
         (* b (* y0 (* j (- (/ (* t y4) y0) x)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.2e+60) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= 8e-196) {
		tmp = b * (fma(a, ((x * y) - (t * z)), (y4 * ((j * t) - (k * y)))) - (y0 * ((j * x) - (k * z))));
	} else if (j <= 3.2e+65) {
		tmp = a * (y3 * (y1 * (z + (-1.0 * ((y * y5) / y1)))));
	} else if (j <= 2.9e+231) {
		tmp = y4 * (-1.0 * (y3 * (y * (((j * y1) / y) - c))));
	} else {
		tmp = b * (y0 * (j * (((t * y4) / y0) - x)));
	}
	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 <= -1.2e+60)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (j <= 8e-196)
		tmp = Float64(b * Float64(fma(a, Float64(Float64(x * y) - Float64(t * z)), Float64(y4 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(y0 * Float64(Float64(j * x) - Float64(k * z)))));
	elseif (j <= 3.2e+65)
		tmp = Float64(a * Float64(y3 * Float64(y1 * Float64(z + Float64(-1.0 * Float64(Float64(y * y5) / y1))))));
	elseif (j <= 2.9e+231)
		tmp = Float64(y4 * Float64(-1.0 * Float64(y3 * Float64(y * Float64(Float64(Float64(j * y1) / y) - c)))));
	else
		tmp = Float64(b * Float64(y0 * Float64(j * Float64(Float64(Float64(t * y4) / y0) - x))));
	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, -1.2e+60], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e-196], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e+65], N[(a * N[(y3 * N[(y1 * N[(z + N[(-1.0 * N[(N[(y * y5), $MachinePrecision] / y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.9e+231], N[(y4 * N[(-1.0 * N[(y3 * N[(y * N[(N[(N[(j * y1), $MachinePrecision] / y), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y0 * N[(j * N[(N[(N[(t * y4), $MachinePrecision] / y0), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.2e60

   1. Initial program 24.1%

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

   2. Taylor expanded in 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 41.9%

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

   5. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 33.6

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 33.6%

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

   if -1.2e60 < j < 8.0000000000000004e-196

   1. Initial program 33.9%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.3%

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

   if 8.0000000000000004e-196 < j < 3.20000000000000007e65

   1. Initial program 33.2%

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

   2. Taylor expanded in 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 33.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

      5. lower-*.f64 26.3

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   7. Applied rewrites 26.3%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   8. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + \color{blue}{-1 \cdot \frac{y \cdot y5}{y1}}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + -1 \cdot \frac{y \cdot y5}{y1}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + -1 \cdot \frac{y \cdot y5}{y1}\right)\right)\right) \]

      5. lift-*.f64 28.7

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot \left(z + -1 \cdot \frac{y \cdot y5}{y1}\right)\right)\right) \]

   10. Applied rewrites 28.7%

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

   if 3.20000000000000007e65 < j < 2.9000000000000001e231

   1. Initial program 27.4%

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

   2. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y3 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 31.5

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 31.5%

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

   8. Taylor expanded in y around inf

      \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - \color{blue}{c}\right)\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

      4. lift-*.f64 35.6

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - c\right)\right)\right)\right) \]

   10. Applied rewrites 35.6%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(y \cdot \left(\frac{j \cdot y1}{y} - \color{blue}{c}\right)\right)\right)\right) \]

   if 2.9000000000000001e231 < j

   1. Initial program 21.2%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 35.6%

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

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   7. Applied rewrites 38.6%

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

   8. Taylor expanded in j around inf

      \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - \color{blue}{x}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

      4. lower-*.f64 51.5

         \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - x\right)\right)\right) \]

   10. Applied rewrites 51.5%

       \[\leadsto b \cdot \left(y0 \cdot \left(j \cdot \left(\frac{t \cdot y4}{y0} - \color{blue}{x}\right)\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 16: 31.7% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{if}\;y1 \leq -1.95 \cdot 10^{+273}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.55 \cdot 10^{+53}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -34000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -3.8 \cdot 10^{-261}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{elif}\;y1 \leq 3.9 \cdot 10^{-116}:\\ \;\;\;\;b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.08 \cdot 10^{+153}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* z (- (* a y3) (* i k))))))
   (if (<= y1 -1.95e+273)
     (* y4 (* c (- (* y y3) (* t y2))))
     (if (<= y1 -1.55e+53)
       (* y4 (* y1 (- (* k y2) (* j y3))))
       (if (<= y1 -34000000000.0)
         t_1
         (if (<= y1 -3.8e-261)
           (* c (* y0 (- (* x y2) (* y3 z))))
           (if (<= y1 3.9e-116)
             (* b (* x (- (* a y) (* j y0))))
             (if (<= y1 1.08e+153)
               (* c (* z (fma -1.0 (* y0 y3) (* i t))))
               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 = y1 * (z * ((a * y3) - (i * k)));
	double tmp;
	if (y1 <= -1.95e+273) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (y1 <= -1.55e+53) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y1 <= -34000000000.0) {
		tmp = t_1;
	} else if (y1 <= -3.8e-261) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else if (y1 <= 3.9e-116) {
		tmp = b * (x * ((a * y) - (j * y0)));
	} else if (y1 <= 1.08e+153) {
		tmp = c * (z * fma(-1.0, (y0 * y3), (i * t)));
	} 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(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))))
	tmp = 0.0
	if (y1 <= -1.95e+273)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y1 <= -1.55e+53)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y1 <= -34000000000.0)
		tmp = t_1;
	elseif (y1 <= -3.8e-261)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	elseif (y1 <= 3.9e-116)
		tmp = Float64(b * Float64(x * Float64(Float64(a * y) - Float64(j * y0))));
	elseif (y1 <= 1.08e+153)
		tmp = Float64(c * Float64(z * fma(-1.0, Float64(y0 * y3), Float64(i * t))));
	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[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.95e+273], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.55e+53], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -34000000000.0], t$95$1, If[LessEqual[y1, -3.8e-261], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.9e-116], N[(b * N[(x * N[(N[(a * y), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.08e+153], N[(c * N[(z * N[(-1.0 * N[(y0 * y3), $MachinePrecision] + N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -1.9500000000000001e273

   1. Initial program 23.8%

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

   2. Taylor expanded in 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 37.3%

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

   5. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]

      4. lift-*.f64 22.6

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]

   7. Applied rewrites 22.6%

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

   if -1.9500000000000001e273 < y1 < -1.5500000000000001e53

   1. Initial program 25.9%

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

   2. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 40.7%

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

   5. Taylor expanded in y1 around inf

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

      4. lift-*.f64 40.5

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

   7. Applied rewrites 40.5%

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

   if -1.5500000000000001e53 < y1 < -3.4e10 or 1.08000000000000006e153 < y1

   1. Initial program 23.0%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 36.3%

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

   5. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 34.9

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

   7. Applied rewrites 34.9%

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

   8. Taylor expanded in y1 around -inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - \color{blue}{i \cdot k}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot \color{blue}{k}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

      5. lower-*.f64 36.4

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

   10. Applied rewrites 36.4%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   if -3.4e10 < y1 < -3.8e-261

   1. Initial program 34.6%

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

   2. Taylor expanded in 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 37.8%

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

   5. Taylor expanded in c around inf

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. 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. lift--.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      5. lift-*.f64 29.8

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   7. Applied rewrites 29.8%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -3.8e-261 < y1 < 3.9000000000000001e-116

   1. Initial program 34.2%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 40.3%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 28.6

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

   7. Applied rewrites 28.6%

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

   if 3.9000000000000001e-116 < y1 < 1.08000000000000006e153

   1. Initial program 31.3%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 39.4%

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

   5. Taylor expanded in c around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 29.6

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

   7. Applied rewrites 29.6%

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

Alternative 17: 31.5% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.95 \cdot 10^{+273}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.55 \cdot 10^{+53}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -34000000000:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -3.8 \cdot 10^{-261}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{elif}\;y1 \leq 1.3 \cdot 10^{-115}:\\ \;\;\;\;b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 4.8 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -1.95e+273)
   (* y4 (* c (- (* y y3) (* t y2))))
   (if (<= y1 -1.55e+53)
     (* y4 (* y1 (- (* k y2) (* j y3))))
     (if (<= y1 -34000000000.0)
       (* y1 (* z (- (* a y3) (* i k))))
       (if (<= y1 -3.8e-261)
         (* c (* y0 (- (* x y2) (* y3 z))))
         (if (<= y1 1.3e-115)
           (* b (* x (- (* a y) (* j y0))))
           (if (<= y1 4.8e+38)
             (* y (* y3 (- (* c y4) (* a y5))))
             (* a (* z (fma -1.0 (* b t) (* y1 y3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -1.95e+273) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (y1 <= -1.55e+53) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y1 <= -34000000000.0) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y1 <= -3.8e-261) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else if (y1 <= 1.3e-115) {
		tmp = b * (x * ((a * y) - (j * y0)));
	} else if (y1 <= 4.8e+38) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else {
		tmp = a * (z * fma(-1.0, (b * t), (y1 * y3)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -1.95e+273)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y1 <= -1.55e+53)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y1 <= -34000000000.0)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (y1 <= -3.8e-261)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	elseif (y1 <= 1.3e-115)
		tmp = Float64(b * Float64(x * Float64(Float64(a * y) - Float64(j * y0))));
	elseif (y1 <= 4.8e+38)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	else
		tmp = Float64(a * Float64(z * fma(-1.0, Float64(b * t), Float64(y1 * y3))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -1.95e+273], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.55e+53], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -34000000000.0], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.8e-261], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.3e-115], N[(b * N[(x * N[(N[(a * y), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.8e+38], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(z * N[(-1.0 * N[(b * t), $MachinePrecision] + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -1.9500000000000001e273

   1. Initial program 23.8%

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

   2. Taylor expanded in 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 37.3%

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

   5. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]

      4. lift-*.f64 22.6

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]

   7. Applied rewrites 22.6%

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

   if -1.9500000000000001e273 < y1 < -1.5500000000000001e53

   1. Initial program 25.9%

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

   2. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 40.7%

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

   5. Taylor expanded in y1 around inf

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

      4. lift-*.f64 40.5

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

   7. Applied rewrites 40.5%

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

   if -1.5500000000000001e53 < y1 < -3.4e10

   1. Initial program 29.8%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

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

   5. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 28.1

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

   7. Applied rewrites 28.1%

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

   8. Taylor expanded in y1 around -inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - \color{blue}{i \cdot k}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot \color{blue}{k}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

      5. lower-*.f64 23.0

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

   10. Applied rewrites 23.0%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   if -3.4e10 < y1 < -3.8e-261

   1. Initial program 34.6%

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

   2. Taylor expanded in 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 37.8%

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

   5. Taylor expanded in c around inf

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. 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. lift--.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      5. lift-*.f64 29.8

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   7. Applied rewrites 29.8%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -3.8e-261 < y1 < 1.30000000000000002e-115

   1. Initial program 34.2%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 40.2%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 28.6

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

   7. Applied rewrites 28.6%

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

   if 1.30000000000000002e-115 < y1 < 4.80000000000000035e38

   1. Initial program 33.5%

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

   2. Taylor expanded in 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 36.8%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - \color{blue}{a \cdot y5}\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot \color{blue}{y5}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lift-*.f64 27.2

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   7. Applied rewrites 27.2%

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 4.80000000000000035e38 < y1

   1. Initial program 24.1%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 38.0%

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

   5. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 35.2

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

   7. Applied rewrites 35.2%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right)} \]
3. Recombined 7 regimes into one program.
4. Add Preprocessing

Alternative 18: 31.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.95 \cdot 10^{+273}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.55 \cdot 10^{+53}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -34000000000:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -3.8 \cdot 10^{-261}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{elif}\;y1 \leq 1.3 \cdot 10^{-115}:\\ \;\;\;\;b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.22 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -1.95e+273)
   (* y4 (* c (- (* y y3) (* t y2))))
   (if (<= y1 -1.55e+53)
     (* y4 (* y1 (- (* k y2) (* j y3))))
     (if (<= y1 -34000000000.0)
       (* y1 (* z (- (* a y3) (* i k))))
       (if (<= y1 -3.8e-261)
         (* c (* y0 (- (* x y2) (* y3 z))))
         (if (<= y1 1.3e-115)
           (* b (* x (- (* a y) (* j y0))))
           (if (<= y1 1.22e+39)
             (* y (* y3 (- (* c y4) (* a y5))))
             (* a (* y3 (- (* y1 z) (* y 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 (y1 <= -1.95e+273) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (y1 <= -1.55e+53) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y1 <= -34000000000.0) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y1 <= -3.8e-261) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else if (y1 <= 1.3e-115) {
		tmp = b * (x * ((a * y) - (j * y0)));
	} else if (y1 <= 1.22e+39) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else {
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	}
	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 <= (-1.95d+273)) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else if (y1 <= (-1.55d+53)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (y1 <= (-34000000000.0d0)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (y1 <= (-3.8d-261)) then
        tmp = c * (y0 * ((x * y2) - (y3 * z)))
    else if (y1 <= 1.3d-115) then
        tmp = b * (x * ((a * y) - (j * y0)))
    else if (y1 <= 1.22d+39) then
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    else
        tmp = a * (y3 * ((y1 * z) - (y * y5)))
    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 <= -1.95e+273) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (y1 <= -1.55e+53) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y1 <= -34000000000.0) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y1 <= -3.8e-261) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else if (y1 <= 1.3e-115) {
		tmp = b * (x * ((a * y) - (j * y0)));
	} else if (y1 <= 1.22e+39) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else {
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	}
	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 <= -1.95e+273:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	elif y1 <= -1.55e+53:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif y1 <= -34000000000.0:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif y1 <= -3.8e-261:
		tmp = c * (y0 * ((x * y2) - (y3 * z)))
	elif y1 <= 1.3e-115:
		tmp = b * (x * ((a * y) - (j * y0)))
	elif y1 <= 1.22e+39:
		tmp = y * (y3 * ((c * y4) - (a * y5)))
	else:
		tmp = a * (y3 * ((y1 * z) - (y * 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 (y1 <= -1.95e+273)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y1 <= -1.55e+53)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y1 <= -34000000000.0)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (y1 <= -3.8e-261)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	elseif (y1 <= 1.3e-115)
		tmp = Float64(b * Float64(x * Float64(Float64(a * y) - Float64(j * y0))));
	elseif (y1 <= 1.22e+39)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	else
		tmp = Float64(a * Float64(y3 * Float64(Float64(y1 * z) - Float64(y * y5))));
	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 <= -1.95e+273)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	elseif (y1 <= -1.55e+53)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (y1 <= -34000000000.0)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (y1 <= -3.8e-261)
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	elseif (y1 <= 1.3e-115)
		tmp = b * (x * ((a * y) - (j * y0)));
	elseif (y1 <= 1.22e+39)
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	else
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	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, -1.95e+273], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.55e+53], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -34000000000.0], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.8e-261], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.3e-115], N[(b * N[(x * N[(N[(a * y), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.22e+39], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(N[(y1 * z), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -1.9500000000000001e273

   1. Initial program 23.8%

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

   2. Taylor expanded in 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 37.3%

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

   5. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]

      4. lift-*.f64 22.6

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]

   7. Applied rewrites 22.6%

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

   if -1.9500000000000001e273 < y1 < -1.5500000000000001e53

   1. Initial program 25.9%

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

   2. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 40.7%

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

   5. Taylor expanded in y1 around inf

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

      4. lift-*.f64 40.5

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

   7. Applied rewrites 40.5%

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

   if -1.5500000000000001e53 < y1 < -3.4e10

   1. Initial program 29.8%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

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

   5. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 28.1

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

   7. Applied rewrites 28.1%

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

   8. Taylor expanded in y1 around -inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - \color{blue}{i \cdot k}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot \color{blue}{k}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

      5. lower-*.f64 23.0

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

   10. Applied rewrites 23.0%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   if -3.4e10 < y1 < -3.8e-261

   1. Initial program 34.6%

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

   2. Taylor expanded in 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 37.8%

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

   5. Taylor expanded in c around inf

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. 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. lift--.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      5. lift-*.f64 29.8

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   7. Applied rewrites 29.8%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -3.8e-261 < y1 < 1.30000000000000002e-115

   1. Initial program 34.2%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 40.2%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 28.6

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

   7. Applied rewrites 28.6%

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

   if 1.30000000000000002e-115 < y1 < 1.22e39

   1. Initial program 33.4%

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

   2. Taylor expanded in 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 36.8%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - \color{blue}{a \cdot y5}\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot \color{blue}{y5}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lift-*.f64 27.0

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   7. Applied rewrites 27.0%

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 1.22e39 < y1

   1. Initial program 24.1%

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

   2. Taylor expanded in 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 36.9%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

      5. lower-*.f64 33.7

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   7. Applied rewrites 33.7%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
3. Recombined 7 regimes into one program.
4. Add Preprocessing

Alternative 19: 31.3% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)\\ \mathbf{if}\;y4 \leq -6.1 \cdot 10^{+38}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -3 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 2.7 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 3 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* z (fma -1.0 (* y0 y3) (* i t))))))
   (if (<= y4 -6.1e+38)
     (* y1 (* y4 (- (* k y2) (* j y3))))
     (if (<= y4 -3e-287)
       t_1
       (if (<= y4 2.7e-56)
         (* b (* x (- (* a y) (* j y0))))
         (if (<= y4 3e+98) t_1 (* -1.0 (* y (* y4 (- (* b k) (* c y3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (z * fma(-1.0, (y0 * y3), (i * t)));
	double tmp;
	if (y4 <= -6.1e+38) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (y4 <= -3e-287) {
		tmp = t_1;
	} else if (y4 <= 2.7e-56) {
		tmp = b * (x * ((a * y) - (j * y0)));
	} else if (y4 <= 3e+98) {
		tmp = t_1;
	} else {
		tmp = -1.0 * (y * (y4 * ((b * k) - (c * y3))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(z * fma(-1.0, Float64(y0 * y3), Float64(i * t))))
	tmp = 0.0
	if (y4 <= -6.1e+38)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y4 <= -3e-287)
		tmp = t_1;
	elseif (y4 <= 2.7e-56)
		tmp = Float64(b * Float64(x * Float64(Float64(a * y) - Float64(j * y0))));
	elseif (y4 <= 3e+98)
		tmp = t_1;
	else
		tmp = Float64(-1.0 * Float64(y * Float64(y4 * Float64(Float64(b * k) - Float64(c * y3)))));
	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[(c * N[(z * N[(-1.0 * N[(y0 * y3), $MachinePrecision] + N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -6.1e+38], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -3e-287], t$95$1, If[LessEqual[y4, 2.7e-56], N[(b * N[(x * N[(N[(a * y), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3e+98], t$95$1, N[(-1.0 * N[(y * N[(y4 * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -6.0999999999999999e38

   1. Initial program 24.6%

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

   2. Taylor expanded in 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 51.7%

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

   5. Taylor expanded in y3 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 34.9

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 34.9%

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

   8. Taylor expanded in y1 around inf

      \[\leadsto y1 \cdot \color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

      5. lower-*.f64 39.7

         \[\leadsto y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   10. Applied rewrites 39.7%

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

   if -6.0999999999999999e38 < y4 < -2.99999999999999992e-287 or 2.69999999999999995e-56 < y4 < 3.0000000000000001e98

   1. Initial program 33.5%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 38.9%

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

   5. Taylor expanded in c around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 27.2

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

   7. Applied rewrites 27.2%

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

   if -2.99999999999999992e-287 < y4 < 2.69999999999999995e-56

   1. Initial program 35.9%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 32.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 26.0

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

   7. Applied rewrites 26.0%

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

   if 3.0000000000000001e98 < y4

   1. Initial program 21.2%

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

   2. Taylor expanded in 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 53.8%

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

   5. Taylor expanded in y around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \color{blue}{\left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \color{blue}{\left(b \cdot k - c \cdot y3\right)}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - \color{blue}{c \cdot y3}\right)\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot \color{blue}{y3}\right)\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right) \]

      6. lower-*.f64 42.7

         \[\leadsto -1 \cdot \left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right) \]

   7. Applied rewrites 42.7%

      \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 20: 31.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -3.3 \cdot 10^{+270}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\\ \mathbf{elif}\;y1 \leq -2.4 \cdot 10^{+53}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -34000000000:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -1.35 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{elif}\;y1 \leq 1.35 \cdot 10^{-115}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;y1 \leq 1.22 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -3.3e+270)
   (* i (* k (- (* y y5) (* y1 z))))
   (if (<= y1 -2.4e+53)
     (* y1 (* y4 (- (* k y2) (* j y3))))
     (if (<= y1 -34000000000.0)
       (* y1 (* z (- (* a y3) (* i k))))
       (if (<= y1 -1.35e-265)
         (* c (* y0 (- (* x y2) (* y3 z))))
         (if (<= y1 1.35e-115)
           (* y3 (* y5 (- (* j y0) (* a y))))
           (if (<= y1 1.22e+39)
             (* y (* y3 (- (* c y4) (* a y5))))
             (* a (* y3 (- (* y1 z) (* y 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 (y1 <= -3.3e+270) {
		tmp = i * (k * ((y * y5) - (y1 * z)));
	} else if (y1 <= -2.4e+53) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (y1 <= -34000000000.0) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y1 <= -1.35e-265) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else if (y1 <= 1.35e-115) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (y1 <= 1.22e+39) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else {
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	}
	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 <= (-3.3d+270)) then
        tmp = i * (k * ((y * y5) - (y1 * z)))
    else if (y1 <= (-2.4d+53)) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (y1 <= (-34000000000.0d0)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (y1 <= (-1.35d-265)) then
        tmp = c * (y0 * ((x * y2) - (y3 * z)))
    else if (y1 <= 1.35d-115) then
        tmp = y3 * (y5 * ((j * y0) - (a * y)))
    else if (y1 <= 1.22d+39) then
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    else
        tmp = a * (y3 * ((y1 * z) - (y * y5)))
    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 <= -3.3e+270) {
		tmp = i * (k * ((y * y5) - (y1 * z)));
	} else if (y1 <= -2.4e+53) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (y1 <= -34000000000.0) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y1 <= -1.35e-265) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else if (y1 <= 1.35e-115) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (y1 <= 1.22e+39) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else {
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	}
	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 <= -3.3e+270:
		tmp = i * (k * ((y * y5) - (y1 * z)))
	elif y1 <= -2.4e+53:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif y1 <= -34000000000.0:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif y1 <= -1.35e-265:
		tmp = c * (y0 * ((x * y2) - (y3 * z)))
	elif y1 <= 1.35e-115:
		tmp = y3 * (y5 * ((j * y0) - (a * y)))
	elif y1 <= 1.22e+39:
		tmp = y * (y3 * ((c * y4) - (a * y5)))
	else:
		tmp = a * (y3 * ((y1 * z) - (y * 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 (y1 <= -3.3e+270)
		tmp = Float64(i * Float64(k * Float64(Float64(y * y5) - Float64(y1 * z))));
	elseif (y1 <= -2.4e+53)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y1 <= -34000000000.0)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (y1 <= -1.35e-265)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	elseif (y1 <= 1.35e-115)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (y1 <= 1.22e+39)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	else
		tmp = Float64(a * Float64(y3 * Float64(Float64(y1 * z) - Float64(y * y5))));
	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 <= -3.3e+270)
		tmp = i * (k * ((y * y5) - (y1 * z)));
	elseif (y1 <= -2.4e+53)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (y1 <= -34000000000.0)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (y1 <= -1.35e-265)
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	elseif (y1 <= 1.35e-115)
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	elseif (y1 <= 1.22e+39)
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	else
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	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, -3.3e+270], N[(i * N[(k * N[(N[(y * y5), $MachinePrecision] - N[(y1 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.4e+53], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -34000000000.0], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.35e-265], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.35e-115], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.22e+39], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(N[(y1 * z), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -3.29999999999999992e270

   1. Initial program 24.1%

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

   2. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 35.6%

      \[\leadsto \color{blue}{k \cdot \left(\mathsf{fma}\left(-1, y \cdot \left(b \cdot y4 - i \cdot y5\right), y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 41.7

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

   7. Applied rewrites 41.7%

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

   if -3.29999999999999992e270 < y1 < -2.4e53

   1. Initial program 25.9%

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

   2. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 40.8%

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

   5. Taylor expanded in y3 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 35.1

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 35.1%

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

   8. Taylor expanded in y1 around inf

      \[\leadsto y1 \cdot \color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

      5. lower-*.f64 36.3

         \[\leadsto y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   10. Applied rewrites 36.3%

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

   if -2.4e53 < y1 < -3.4e10

   1. Initial program 29.6%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 37.6%

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

   5. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 28.6

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

   7. Applied rewrites 28.6%

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

   8. Taylor expanded in y1 around -inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - \color{blue}{i \cdot k}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot \color{blue}{k}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

      5. lower-*.f64 23.2

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

   10. Applied rewrites 23.2%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   if -3.4e10 < y1 < -1.3500000000000001e-265

   1. Initial program 34.7%

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

   2. Taylor expanded in 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 37.9%

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

   5. Taylor expanded in c around inf

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. 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. lift--.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      5. lift-*.f64 29.9

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   7. Applied rewrites 29.9%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -1.3500000000000001e-265 < y1 < 1.35e-115

   1. Initial program 34.0%

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

   2. Taylor expanded in 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 37.4%

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

   5. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 27.4

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 27.4%

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

   if 1.35e-115 < y1 < 1.22e39

   1. Initial program 33.4%

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

   2. Taylor expanded in 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 36.8%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - \color{blue}{a \cdot y5}\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot \color{blue}{y5}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lift-*.f64 27.0

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   7. Applied rewrites 27.0%

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 1.22e39 < y1

   1. Initial program 24.1%

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

   2. Taylor expanded in 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 36.9%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

      5. lower-*.f64 33.7

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   7. Applied rewrites 33.7%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
3. Recombined 7 regimes into one program.
4. Add Preprocessing

Alternative 21: 30.2% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.12 \cdot 10^{-30}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-190}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-108}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{+124}:\\ \;\;\;\;i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+231}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.12e-30)
   (* y3 (* y5 (- (* j y0) (* a y))))
   (if (<= j 7.8e-190)
     (* k (* z (- (* b y0) (* i y1))))
     (if (<= j 4e-108)
       (* a (* y3 (- (* y1 z) (* y y5))))
       (if (<= j 1.35e+124)
         (* i (* z (- (* c t) (* k y1))))
         (if (<= j 1.48e+231)
           (* y4 (* -1.0 (* y3 (* j y1))))
           (* b (* x (* -1.0 (* j 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 (j <= -1.12e-30) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= 7.8e-190) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (j <= 4e-108) {
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	} else if (j <= 1.35e+124) {
		tmp = i * (z * ((c * t) - (k * y1)));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	} else {
		tmp = b * (x * (-1.0 * (j * 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 (j <= (-1.12d-30)) then
        tmp = y3 * (y5 * ((j * y0) - (a * y)))
    else if (j <= 7.8d-190) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (j <= 4d-108) then
        tmp = a * (y3 * ((y1 * z) - (y * y5)))
    else if (j <= 1.35d+124) then
        tmp = i * (z * ((c * t) - (k * y1)))
    else if (j <= 1.48d+231) then
        tmp = y4 * ((-1.0d0) * (y3 * (j * y1)))
    else
        tmp = b * (x * ((-1.0d0) * (j * 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 (j <= -1.12e-30) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= 7.8e-190) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (j <= 4e-108) {
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	} else if (j <= 1.35e+124) {
		tmp = i * (z * ((c * t) - (k * y1)));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	} else {
		tmp = b * (x * (-1.0 * (j * 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 j <= -1.12e-30:
		tmp = y3 * (y5 * ((j * y0) - (a * y)))
	elif j <= 7.8e-190:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif j <= 4e-108:
		tmp = a * (y3 * ((y1 * z) - (y * y5)))
	elif j <= 1.35e+124:
		tmp = i * (z * ((c * t) - (k * y1)))
	elif j <= 1.48e+231:
		tmp = y4 * (-1.0 * (y3 * (j * y1)))
	else:
		tmp = b * (x * (-1.0 * (j * 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 (j <= -1.12e-30)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (j <= 7.8e-190)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (j <= 4e-108)
		tmp = Float64(a * Float64(y3 * Float64(Float64(y1 * z) - Float64(y * y5))));
	elseif (j <= 1.35e+124)
		tmp = Float64(i * Float64(z * Float64(Float64(c * t) - Float64(k * y1))));
	elseif (j <= 1.48e+231)
		tmp = Float64(y4 * Float64(-1.0 * Float64(y3 * Float64(j * y1))));
	else
		tmp = Float64(b * Float64(x * Float64(-1.0 * Float64(j * 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 (j <= -1.12e-30)
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	elseif (j <= 7.8e-190)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (j <= 4e-108)
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	elseif (j <= 1.35e+124)
		tmp = i * (z * ((c * t) - (k * y1)));
	elseif (j <= 1.48e+231)
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	else
		tmp = b * (x * (-1.0 * (j * 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[j, -1.12e-30], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.8e-190], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4e-108], N[(a * N[(y3 * N[(N[(y1 * z), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.35e+124], N[(i * N[(z * N[(N[(c * t), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.48e+231], N[(y4 * N[(-1.0 * N[(y3 * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(x * N[(-1.0 * N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.12e-30

   1. Initial program 25.7%

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

   2. Taylor expanded in 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 40.9%

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

   5. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot \color{blue}{y}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 31.2

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 31.2%

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]

   if -1.12e-30 < j < 7.7999999999999999e-190

   1. Initial program 34.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 39.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + \color{blue}{y1 \cdot y3}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot \color{blue}{t}, y1 \cdot y3\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

      5. lower-*.f64 27.8

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

   7. Applied rewrites 27.8%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right)} \]

   8. Taylor expanded in k around -inf

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot \color{blue}{y1}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      5. lower-*.f64 27.1

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   10. Applied rewrites 27.1%

       \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   if 7.7999999999999999e-190 < j < 4.00000000000000016e-108

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 33.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

      5. lower-*.f64 25.9

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   7. Applied rewrites 25.9%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if 4.00000000000000016e-108 < j < 1.34999999999999989e124

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 36.8%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in i around -inf

      \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t - k \cdot y1\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \left(c \cdot t - \color{blue}{k \cdot y1}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \left(c \cdot t - k \cdot \color{blue}{y1}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right) \]

      5. lower-*.f64 28.0

         \[\leadsto i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right) \]

   7. Applied rewrites 28.0%

      \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if 1.34999999999999989e124 < j < 1.47999999999999997e231

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   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 37.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y1 - c \cdot y\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - \color{blue}{c \cdot y}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot \color{blue}{y}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 34.1

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 34.1%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 28.5

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]

   10. Applied rewrites 28.5%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]

   if 1.47999999999999997e231 < j

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 40.0

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 40.0%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

      2. lift-*.f64 37.0

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

   10. Applied rewrites 37.0%

       \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 22: 29.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -5.4 \cdot 10^{+186}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;y3 \leq 1.45 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -5.4e+186)
   (* y3 (* y5 (- (* j y0) (* a y))))
   (if (<= y3 1.45e+48)
     (* b (* x (- (* a y) (* j y0))))
     (* c (* y0 (- (* 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 tmp;
	if (y3 <= -5.4e+186) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (y3 <= 1.45e+48) {
		tmp = b * (x * ((a * y) - (j * y0)));
	} else {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y3 <= (-5.4d+186)) then
        tmp = y3 * (y5 * ((j * y0) - (a * y)))
    else if (y3 <= 1.45d+48) then
        tmp = b * (x * ((a * y) - (j * y0)))
    else
        tmp = c * (y0 * ((x * y2) - (y3 * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -5.4e+186) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (y3 <= 1.45e+48) {
		tmp = b * (x * ((a * y) - (j * y0)));
	} else {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -5.4e+186:
		tmp = y3 * (y5 * ((j * y0) - (a * y)))
	elif y3 <= 1.45e+48:
		tmp = b * (x * ((a * y) - (j * y0)))
	else:
		tmp = c * (y0 * ((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)
	tmp = 0.0
	if (y3 <= -5.4e+186)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (y3 <= 1.45e+48)
		tmp = Float64(b * Float64(x * Float64(Float64(a * y) - Float64(j * y0))));
	else
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -5.4e+186)
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	elseif (y3 <= 1.45e+48)
		tmp = b * (x * ((a * y) - (j * y0)));
	else
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -5.4e+186], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.45e+48], N[(b * N[(x * N[(N[(a * y), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y3 < -5.3999999999999998e186

   1. Initial program 20.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 59.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in y5 around -inf

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \color{blue}{\left(j \cdot y0 - a \cdot y\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - \color{blue}{a \cdot y}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot \color{blue}{y}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 41.7

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 41.7%

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]

   if -5.3999999999999998e186 < y3 < 1.4499999999999999e48

   1. Initial program 32.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 37.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 27.7

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 27.7%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   if 1.4499999999999999e48 < y3

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 34.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in c around inf

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. 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. lift--.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      5. lift-*.f64 33.1

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   7. Applied rewrites 33.1%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 23: 29.1% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3 \cdot 10^{+100}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-108}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{+124}:\\ \;\;\;\;i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+231}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -3e+100)
   (* y3 (* y5 (- (* j y0) (* a y))))
   (if (<= j 6.4e-108)
     (* y (* y3 (- (* c y4) (* a y5))))
     (if (<= j 1.35e+124)
       (* i (* z (- (* c t) (* k y1))))
       (if (<= j 1.48e+231)
         (* y4 (* -1.0 (* y3 (* j y1))))
         (* b (* x (* -1.0 (* j 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 (j <= -3e+100) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= 6.4e-108) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (j <= 1.35e+124) {
		tmp = i * (z * ((c * t) - (k * y1)));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	} else {
		tmp = b * (x * (-1.0 * (j * 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 (j <= (-3d+100)) then
        tmp = y3 * (y5 * ((j * y0) - (a * y)))
    else if (j <= 6.4d-108) then
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    else if (j <= 1.35d+124) then
        tmp = i * (z * ((c * t) - (k * y1)))
    else if (j <= 1.48d+231) then
        tmp = y4 * ((-1.0d0) * (y3 * (j * y1)))
    else
        tmp = b * (x * ((-1.0d0) * (j * 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 (j <= -3e+100) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= 6.4e-108) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (j <= 1.35e+124) {
		tmp = i * (z * ((c * t) - (k * y1)));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	} else {
		tmp = b * (x * (-1.0 * (j * 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 j <= -3e+100:
		tmp = y3 * (y5 * ((j * y0) - (a * y)))
	elif j <= 6.4e-108:
		tmp = y * (y3 * ((c * y4) - (a * y5)))
	elif j <= 1.35e+124:
		tmp = i * (z * ((c * t) - (k * y1)))
	elif j <= 1.48e+231:
		tmp = y4 * (-1.0 * (y3 * (j * y1)))
	else:
		tmp = b * (x * (-1.0 * (j * 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 (j <= -3e+100)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (j <= 6.4e-108)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (j <= 1.35e+124)
		tmp = Float64(i * Float64(z * Float64(Float64(c * t) - Float64(k * y1))));
	elseif (j <= 1.48e+231)
		tmp = Float64(y4 * Float64(-1.0 * Float64(y3 * Float64(j * y1))));
	else
		tmp = Float64(b * Float64(x * Float64(-1.0 * Float64(j * 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 (j <= -3e+100)
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	elseif (j <= 6.4e-108)
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	elseif (j <= 1.35e+124)
		tmp = i * (z * ((c * t) - (k * y1)));
	elseif (j <= 1.48e+231)
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	else
		tmp = b * (x * (-1.0 * (j * 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[j, -3e+100], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.4e-108], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.35e+124], N[(i * N[(z * N[(N[(c * t), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.48e+231], N[(y4 * N[(-1.0 * N[(y3 * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(x * N[(-1.0 * N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.99999999999999985e100

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 42.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in y5 around -inf

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \color{blue}{\left(j \cdot y0 - a \cdot y\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - \color{blue}{a \cdot y}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot \color{blue}{y}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 34.1

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 34.1%

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]

   if -2.99999999999999985e100 < j < 6.3999999999999999e-108

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 34.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - \color{blue}{a \cdot y5}\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot \color{blue}{y5}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lift-*.f64 26.8

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   7. Applied rewrites 26.8%

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 6.3999999999999999e-108 < j < 1.34999999999999989e124

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 36.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in i around -inf

      \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t - k \cdot y1\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \left(c \cdot t - \color{blue}{k \cdot y1}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \left(c \cdot t - k \cdot \color{blue}{y1}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right) \]

      5. lower-*.f64 28.0

         \[\leadsto i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right) \]

   7. Applied rewrites 28.0%

      \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if 1.34999999999999989e124 < j < 1.47999999999999997e231

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   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 37.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y1 - c \cdot y\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - \color{blue}{c \cdot y}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot \color{blue}{y}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 34.1

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 34.1%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 28.5

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]

   10. Applied rewrites 28.5%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]

   if 1.47999999999999997e231 < j

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 40.0

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 40.0%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

      2. lift-*.f64 37.0

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

   10. Applied rewrites 37.0%

       \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 24: 29.1% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3 \cdot 10^{+100}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+231}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -3e+100)
   (* y3 (* y5 (- (* j y0) (* a y))))
   (if (<= j 1.02e+76)
     (* y (* y3 (- (* c y4) (* a y5))))
     (if (<= j 1.48e+231)
       (* y4 (* -1.0 (* y3 (* j y1))))
       (* b (* x (* -1.0 (* j 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 (j <= -3e+100) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= 1.02e+76) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	} else {
		tmp = b * (x * (-1.0 * (j * 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 (j <= (-3d+100)) then
        tmp = y3 * (y5 * ((j * y0) - (a * y)))
    else if (j <= 1.02d+76) then
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    else if (j <= 1.48d+231) then
        tmp = y4 * ((-1.0d0) * (y3 * (j * y1)))
    else
        tmp = b * (x * ((-1.0d0) * (j * 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 (j <= -3e+100) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= 1.02e+76) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	} else {
		tmp = b * (x * (-1.0 * (j * 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 j <= -3e+100:
		tmp = y3 * (y5 * ((j * y0) - (a * y)))
	elif j <= 1.02e+76:
		tmp = y * (y3 * ((c * y4) - (a * y5)))
	elif j <= 1.48e+231:
		tmp = y4 * (-1.0 * (y3 * (j * y1)))
	else:
		tmp = b * (x * (-1.0 * (j * 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 (j <= -3e+100)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (j <= 1.02e+76)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (j <= 1.48e+231)
		tmp = Float64(y4 * Float64(-1.0 * Float64(y3 * Float64(j * y1))));
	else
		tmp = Float64(b * Float64(x * Float64(-1.0 * Float64(j * 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 (j <= -3e+100)
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	elseif (j <= 1.02e+76)
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	elseif (j <= 1.48e+231)
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	else
		tmp = b * (x * (-1.0 * (j * 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[j, -3e+100], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.02e+76], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.48e+231], N[(y4 * N[(-1.0 * N[(y3 * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(x * N[(-1.0 * N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.99999999999999985e100

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 42.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in y5 around -inf

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \color{blue}{\left(j \cdot y0 - a \cdot y\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - \color{blue}{a \cdot y}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot \color{blue}{y}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 34.1

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 34.1%

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]

   if -2.99999999999999985e100 < j < 1.02000000000000007e76

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 34.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - \color{blue}{a \cdot y5}\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot \color{blue}{y5}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lift-*.f64 26.3

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   7. Applied rewrites 26.3%

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 1.02000000000000007e76 < j < 1.47999999999999997e231

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   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 37.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y1 - c \cdot y\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - \color{blue}{c \cdot y}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot \color{blue}{y}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 32.1

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 32.1%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 26.5

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]

   10. Applied rewrites 26.5%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]

   if 1.47999999999999997e231 < j

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 40.0

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 40.0%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

      2. lift-*.f64 37.0

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

   10. Applied rewrites 37.0%

       \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 25: 28.4% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{+64}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+231}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.4e+64)
   (* y3 (* y5 (- (* j y0) (* a y))))
   (if (<= j 3.7e+231)
     (* c (* y0 (- (* x y2) (* y3 z))))
     (* b (* x (* -1.0 (* j 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 (j <= -1.4e+64) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= 3.7e+231) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else {
		tmp = b * (x * (-1.0 * (j * 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 (j <= (-1.4d+64)) then
        tmp = y3 * (y5 * ((j * y0) - (a * y)))
    else if (j <= 3.7d+231) then
        tmp = c * (y0 * ((x * y2) - (y3 * z)))
    else
        tmp = b * (x * ((-1.0d0) * (j * 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 (j <= -1.4e+64) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (j <= 3.7e+231) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else {
		tmp = b * (x * (-1.0 * (j * 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 j <= -1.4e+64:
		tmp = y3 * (y5 * ((j * y0) - (a * y)))
	elif j <= 3.7e+231:
		tmp = c * (y0 * ((x * y2) - (y3 * z)))
	else:
		tmp = b * (x * (-1.0 * (j * 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 (j <= -1.4e+64)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (j <= 3.7e+231)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	else
		tmp = Float64(b * Float64(x * Float64(-1.0 * Float64(j * 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 (j <= -1.4e+64)
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	elseif (j <= 3.7e+231)
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	else
		tmp = b * (x * (-1.0 * (j * 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[j, -1.4e+64], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.7e+231], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(x * N[(-1.0 * N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.40000000000000012e64

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 42.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in y5 around -inf

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \color{blue}{\left(j \cdot y0 - a \cdot y\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - \color{blue}{a \cdot y}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot \color{blue}{y}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 33.6

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 33.6%

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]

   if -1.40000000000000012e64 < j < 3.7e231

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - \color{blue}{b \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in c around inf

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. 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. lift--.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      5. lift-*.f64 27.2

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   7. Applied rewrites 27.2%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 3.7e231 < j

   1. Initial program 21.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 39.9

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 39.9%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

      2. lift-*.f64 36.9

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

   10. Applied rewrites 36.9%

       \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 26: 28.0% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right)\\ \mathbf{if}\;j \leq -6.8 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+231}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (* -1.0 (* j y0))))))
   (if (<= j -6.8e+217)
     t_1
     (if (<= j 1.02e+76)
       (* y (* y3 (- (* c y4) (* a y5))))
       (if (<= j 1.48e+231) (* y4 (* -1.0 (* y3 (* j y1)))) 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 * (x * (-1.0 * (j * y0)));
	double tmp;
	if (j <= -6.8e+217) {
		tmp = t_1;
	} else if (j <= 1.02e+76) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	} 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 * (x * ((-1.0d0) * (j * y0)))
    if (j <= (-6.8d+217)) then
        tmp = t_1
    else if (j <= 1.02d+76) then
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    else if (j <= 1.48d+231) then
        tmp = y4 * ((-1.0d0) * (y3 * (j * y1)))
    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 * (x * (-1.0 * (j * y0)));
	double tmp;
	if (j <= -6.8e+217) {
		tmp = t_1;
	} else if (j <= 1.02e+76) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	} 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 * (x * (-1.0 * (j * y0)))
	tmp = 0
	if j <= -6.8e+217:
		tmp = t_1
	elif j <= 1.02e+76:
		tmp = y * (y3 * ((c * y4) - (a * y5)))
	elif j <= 1.48e+231:
		tmp = y4 * (-1.0 * (y3 * (j * y1)))
	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(x * Float64(-1.0 * Float64(j * y0))))
	tmp = 0.0
	if (j <= -6.8e+217)
		tmp = t_1;
	elseif (j <= 1.02e+76)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (j <= 1.48e+231)
		tmp = Float64(y4 * Float64(-1.0 * Float64(y3 * Float64(j * y1))));
	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 * (x * (-1.0 * (j * y0)));
	tmp = 0.0;
	if (j <= -6.8e+217)
		tmp = t_1;
	elseif (j <= 1.02e+76)
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	elseif (j <= 1.48e+231)
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	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[(x * N[(-1.0 * N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.8e+217], t$95$1, If[LessEqual[j, 1.02e+76], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.48e+231], N[(y4 * N[(-1.0 * N[(y3 * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -6.7999999999999998e217 or 1.47999999999999997e231 < j

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 36.3%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 38.6

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 38.6%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

      2. lift-*.f64 36.6

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

   10. Applied rewrites 36.6%

       \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]

   if -6.7999999999999998e217 < j < 1.02000000000000007e76

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 35.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - \color{blue}{a \cdot y5}\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot \color{blue}{y5}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lift-*.f64 26.2

         \[\leadsto y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 1.02000000000000007e76 < j < 1.47999999999999997e231

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   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 37.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y1 - c \cdot y\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - \color{blue}{c \cdot y}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot \color{blue}{y}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 32.1

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 32.1%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 26.5

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]

   10. Applied rewrites 26.5%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 27: 27.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right)\\ \mathbf{if}\;j \leq -6.5 \cdot 10^{+216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+231}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (* -1.0 (* j y0))))))
   (if (<= j -6.5e+216)
     t_1
     (if (<= j 3.9e+66)
       (* a (* y3 (- (* y1 z) (* y y5))))
       (if (<= j 1.48e+231) (* y4 (* -1.0 (* y3 (* j y1)))) 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 * (x * (-1.0 * (j * y0)));
	double tmp;
	if (j <= -6.5e+216) {
		tmp = t_1;
	} else if (j <= 3.9e+66) {
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	} 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 * (x * ((-1.0d0) * (j * y0)))
    if (j <= (-6.5d+216)) then
        tmp = t_1
    else if (j <= 3.9d+66) then
        tmp = a * (y3 * ((y1 * z) - (y * y5)))
    else if (j <= 1.48d+231) then
        tmp = y4 * ((-1.0d0) * (y3 * (j * y1)))
    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 * (x * (-1.0 * (j * y0)));
	double tmp;
	if (j <= -6.5e+216) {
		tmp = t_1;
	} else if (j <= 3.9e+66) {
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	} 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 * (x * (-1.0 * (j * y0)))
	tmp = 0
	if j <= -6.5e+216:
		tmp = t_1
	elif j <= 3.9e+66:
		tmp = a * (y3 * ((y1 * z) - (y * y5)))
	elif j <= 1.48e+231:
		tmp = y4 * (-1.0 * (y3 * (j * y1)))
	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(x * Float64(-1.0 * Float64(j * y0))))
	tmp = 0.0
	if (j <= -6.5e+216)
		tmp = t_1;
	elseif (j <= 3.9e+66)
		tmp = Float64(a * Float64(y3 * Float64(Float64(y1 * z) - Float64(y * y5))));
	elseif (j <= 1.48e+231)
		tmp = Float64(y4 * Float64(-1.0 * Float64(y3 * Float64(j * y1))));
	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 * (x * (-1.0 * (j * y0)));
	tmp = 0.0;
	if (j <= -6.5e+216)
		tmp = t_1;
	elseif (j <= 3.9e+66)
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	elseif (j <= 1.48e+231)
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	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[(x * N[(-1.0 * N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.5e+216], t$95$1, If[LessEqual[j, 3.9e+66], N[(a * N[(y3 * N[(N[(y1 * z), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.48e+231], N[(y4 * N[(-1.0 * N[(y3 * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -6.50000000000000029e216 or 1.47999999999999997e231 < j

   1. Initial program 20.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 36.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 38.7

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 38.7%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

      2. lift-*.f64 36.7

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

   10. Applied rewrites 36.7%

       \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]

   if -6.50000000000000029e216 < j < 3.9000000000000004e66

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 35.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

      5. lower-*.f64 26.5

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   7. Applied rewrites 26.5%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if 3.9000000000000004e66 < j < 1.47999999999999997e231

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 37.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y1 - c \cdot y\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - \color{blue}{c \cdot y}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot \color{blue}{y}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 31.6

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 31.6%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 26.1

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]

   10. Applied rewrites 26.1%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 28: 22.5% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right)\\ \mathbf{if}\;j \leq -8.4 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-189}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 8.4 \cdot 10^{-190}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(-1 \cdot \left(y0 \cdot y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.55 \cdot 10^{-89}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+231}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (* -1.0 (* j y0))))))
   (if (<= j -8.4e+102)
     t_1
     (if (<= j -4.1e-189)
       (* y4 (* c (* y y3)))
       (if (<= j 8.4e-190)
         (* k (* y2 (* -1.0 (* y0 y5))))
         (if (<= j 2.55e-89)
           (* a (* y3 (* y1 z)))
           (if (<= j 1.4e+79)
             (* b (* a (* x y)))
             (if (<= j 1.48e+231) (* y4 (* -1.0 (* j (* y1 y3)))) 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 * (x * (-1.0 * (j * y0)));
	double tmp;
	if (j <= -8.4e+102) {
		tmp = t_1;
	} else if (j <= -4.1e-189) {
		tmp = y4 * (c * (y * y3));
	} else if (j <= 8.4e-190) {
		tmp = k * (y2 * (-1.0 * (y0 * y5)));
	} else if (j <= 2.55e-89) {
		tmp = a * (y3 * (y1 * z));
	} else if (j <= 1.4e+79) {
		tmp = b * (a * (x * y));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (j * (y1 * y3)));
	} 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 * (x * ((-1.0d0) * (j * y0)))
    if (j <= (-8.4d+102)) then
        tmp = t_1
    else if (j <= (-4.1d-189)) then
        tmp = y4 * (c * (y * y3))
    else if (j <= 8.4d-190) then
        tmp = k * (y2 * ((-1.0d0) * (y0 * y5)))
    else if (j <= 2.55d-89) then
        tmp = a * (y3 * (y1 * z))
    else if (j <= 1.4d+79) then
        tmp = b * (a * (x * y))
    else if (j <= 1.48d+231) then
        tmp = y4 * ((-1.0d0) * (j * (y1 * y3)))
    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 * (x * (-1.0 * (j * y0)));
	double tmp;
	if (j <= -8.4e+102) {
		tmp = t_1;
	} else if (j <= -4.1e-189) {
		tmp = y4 * (c * (y * y3));
	} else if (j <= 8.4e-190) {
		tmp = k * (y2 * (-1.0 * (y0 * y5)));
	} else if (j <= 2.55e-89) {
		tmp = a * (y3 * (y1 * z));
	} else if (j <= 1.4e+79) {
		tmp = b * (a * (x * y));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (j * (y1 * y3)));
	} 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 * (x * (-1.0 * (j * y0)))
	tmp = 0
	if j <= -8.4e+102:
		tmp = t_1
	elif j <= -4.1e-189:
		tmp = y4 * (c * (y * y3))
	elif j <= 8.4e-190:
		tmp = k * (y2 * (-1.0 * (y0 * y5)))
	elif j <= 2.55e-89:
		tmp = a * (y3 * (y1 * z))
	elif j <= 1.4e+79:
		tmp = b * (a * (x * y))
	elif j <= 1.48e+231:
		tmp = y4 * (-1.0 * (j * (y1 * y3)))
	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(x * Float64(-1.0 * Float64(j * y0))))
	tmp = 0.0
	if (j <= -8.4e+102)
		tmp = t_1;
	elseif (j <= -4.1e-189)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (j <= 8.4e-190)
		tmp = Float64(k * Float64(y2 * Float64(-1.0 * Float64(y0 * y5))));
	elseif (j <= 2.55e-89)
		tmp = Float64(a * Float64(y3 * Float64(y1 * z)));
	elseif (j <= 1.4e+79)
		tmp = Float64(b * Float64(a * Float64(x * y)));
	elseif (j <= 1.48e+231)
		tmp = Float64(y4 * Float64(-1.0 * Float64(j * Float64(y1 * y3))));
	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 * (x * (-1.0 * (j * y0)));
	tmp = 0.0;
	if (j <= -8.4e+102)
		tmp = t_1;
	elseif (j <= -4.1e-189)
		tmp = y4 * (c * (y * y3));
	elseif (j <= 8.4e-190)
		tmp = k * (y2 * (-1.0 * (y0 * y5)));
	elseif (j <= 2.55e-89)
		tmp = a * (y3 * (y1 * z));
	elseif (j <= 1.4e+79)
		tmp = b * (a * (x * y));
	elseif (j <= 1.48e+231)
		tmp = y4 * (-1.0 * (j * (y1 * y3)));
	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[(x * N[(-1.0 * N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.4e+102], t$95$1, If[LessEqual[j, -4.1e-189], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.4e-190], N[(k * N[(y2 * N[(-1.0 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.55e-89], N[(a * N[(y3 * N[(y1 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.4e+79], N[(b * N[(a * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.48e+231], N[(y4 * N[(-1.0 * N[(j * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -8.40000000000000006e102 or 1.47999999999999997e231 < j

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 37.0%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 36.2

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 36.2%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

      2. lift-*.f64 32.8

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

   10. Applied rewrites 32.8%

       \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]

   if -8.40000000000000006e102 < j < -4.1000000000000003e-189

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 37.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y1 - c \cdot y\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - \color{blue}{c \cdot y}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot \color{blue}{y}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 23.8

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 23.8%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) \]

      2. lower-*.f64 17.4

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) \]

   10. Applied rewrites 17.4%

       \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) \]

   if -4.1000000000000003e-189 < j < 8.39999999999999966e-190

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{-1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

   4. Applied rewrites 37.8%

      \[\leadsto \color{blue}{k \cdot \left(\mathsf{fma}\left(-1, y \cdot \left(b \cdot y4 - i \cdot y5\right), y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y2 around inf

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}\right) \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot \color{blue}{y5}\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

      4. lift-*.f64 26.7

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - \color{blue}{y0 \cdot y5}\right)\right) \]

   7. Applied rewrites 26.7%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}\right) \]

   8. Taylor expanded in y0 around inf

      \[\leadsto k \cdot \left(y2 \cdot \left(-1 \cdot \left(y0 \cdot \color{blue}{y5}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(-1 \cdot \left(y0 \cdot y5\right)\right)\right) \]

      2. lift-*.f64 17.1

         \[\leadsto k \cdot \left(y2 \cdot \left(-1 \cdot \left(y0 \cdot y5\right)\right)\right) \]

   10. Applied rewrites 17.1%

       \[\leadsto k \cdot \left(y2 \cdot \left(-1 \cdot \left(y0 \cdot \color{blue}{y5}\right)\right)\right) \]

   if 8.39999999999999966e-190 < j < 2.55000000000000002e-89

   1. Initial program 35.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 35.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

      5. lower-*.f64 26.5

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   7. Applied rewrites 26.5%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 18.3

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]

   10. Applied rewrites 18.3%

       \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]

   if 2.55000000000000002e-89 < j < 1.4000000000000001e79

   1. Initial program 31.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 36.0%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 25.3

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 25.3%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto b \cdot \left(a \cdot \left(x \cdot \color{blue}{y}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(a \cdot \left(x \cdot y\right)\right) \]

      2. lift-*.f64 18.4

         \[\leadsto b \cdot \left(a \cdot \left(x \cdot y\right)\right) \]

   10. Applied rewrites 18.4%

       \[\leadsto b \cdot \left(a \cdot \left(x \cdot \color{blue}{y}\right)\right) \]

   if 1.4000000000000001e79 < j < 1.47999999999999997e231

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

   4. Applied rewrites 37.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y1 - c \cdot y\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - \color{blue}{c \cdot y}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot \color{blue}{y}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 32.0

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 32.0%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot \color{blue}{y3}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right)\right) \]

      2. lift-*.f64 23.5

         \[\leadsto y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right)\right) \]

   10. Applied rewrites 23.5%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot \color{blue}{y3}\right)\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 29: 22.5% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right)\\ \mathbf{if}\;j \leq -8.4 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-189}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 8.4 \cdot 10^{-190}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(-1 \cdot \left(y0 \cdot y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.55 \cdot 10^{-89}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+101}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (* -1.0 (* j y0))))))
   (if (<= j -8.4e+102)
     t_1
     (if (<= j -4.1e-189)
       (* y4 (* c (* y y3)))
       (if (<= j 8.4e-190)
         (* k (* y2 (* -1.0 (* y0 y5))))
         (if (<= j 2.55e-89)
           (* a (* y3 (* y1 z)))
           (if (<= j 4.2e+101) (* b (* a (* x y))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * (-1.0 * (j * y0)));
	double tmp;
	if (j <= -8.4e+102) {
		tmp = t_1;
	} else if (j <= -4.1e-189) {
		tmp = y4 * (c * (y * y3));
	} else if (j <= 8.4e-190) {
		tmp = k * (y2 * (-1.0 * (y0 * y5)));
	} else if (j <= 2.55e-89) {
		tmp = a * (y3 * (y1 * z));
	} else if (j <= 4.2e+101) {
		tmp = b * (a * (x * y));
	} 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 * (x * ((-1.0d0) * (j * y0)))
    if (j <= (-8.4d+102)) then
        tmp = t_1
    else if (j <= (-4.1d-189)) then
        tmp = y4 * (c * (y * y3))
    else if (j <= 8.4d-190) then
        tmp = k * (y2 * ((-1.0d0) * (y0 * y5)))
    else if (j <= 2.55d-89) then
        tmp = a * (y3 * (y1 * z))
    else if (j <= 4.2d+101) then
        tmp = b * (a * (x * y))
    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 * (x * (-1.0 * (j * y0)));
	double tmp;
	if (j <= -8.4e+102) {
		tmp = t_1;
	} else if (j <= -4.1e-189) {
		tmp = y4 * (c * (y * y3));
	} else if (j <= 8.4e-190) {
		tmp = k * (y2 * (-1.0 * (y0 * y5)));
	} else if (j <= 2.55e-89) {
		tmp = a * (y3 * (y1 * z));
	} else if (j <= 4.2e+101) {
		tmp = b * (a * (x * y));
	} 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 * (x * (-1.0 * (j * y0)))
	tmp = 0
	if j <= -8.4e+102:
		tmp = t_1
	elif j <= -4.1e-189:
		tmp = y4 * (c * (y * y3))
	elif j <= 8.4e-190:
		tmp = k * (y2 * (-1.0 * (y0 * y5)))
	elif j <= 2.55e-89:
		tmp = a * (y3 * (y1 * z))
	elif j <= 4.2e+101:
		tmp = b * (a * (x * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(x * Float64(-1.0 * Float64(j * y0))))
	tmp = 0.0
	if (j <= -8.4e+102)
		tmp = t_1;
	elseif (j <= -4.1e-189)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (j <= 8.4e-190)
		tmp = Float64(k * Float64(y2 * Float64(-1.0 * Float64(y0 * y5))));
	elseif (j <= 2.55e-89)
		tmp = Float64(a * Float64(y3 * Float64(y1 * z)));
	elseif (j <= 4.2e+101)
		tmp = Float64(b * Float64(a * Float64(x * y)));
	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 * (x * (-1.0 * (j * y0)));
	tmp = 0.0;
	if (j <= -8.4e+102)
		tmp = t_1;
	elseif (j <= -4.1e-189)
		tmp = y4 * (c * (y * y3));
	elseif (j <= 8.4e-190)
		tmp = k * (y2 * (-1.0 * (y0 * y5)));
	elseif (j <= 2.55e-89)
		tmp = a * (y3 * (y1 * z));
	elseif (j <= 4.2e+101)
		tmp = b * (a * (x * y));
	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[(x * N[(-1.0 * N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.4e+102], t$95$1, If[LessEqual[j, -4.1e-189], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.4e-190], N[(k * N[(y2 * N[(-1.0 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.55e-89], N[(a * N[(y3 * N[(y1 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.2e+101], N[(b * N[(a * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -8.40000000000000006e102 or 4.2e101 < j

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 35.6

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 35.6%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

      2. lift-*.f64 31.1

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

   10. Applied rewrites 31.1%

       \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]

   if -8.40000000000000006e102 < j < -4.1000000000000003e-189

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 37.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y1 - c \cdot y\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - \color{blue}{c \cdot y}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot \color{blue}{y}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 23.8

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 23.8%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) \]

      2. lower-*.f64 17.4

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) \]

   10. Applied rewrites 17.4%

       \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) \]

   if -4.1000000000000003e-189 < j < 8.39999999999999966e-190

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{-1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

   4. Applied rewrites 37.8%

      \[\leadsto \color{blue}{k \cdot \left(\mathsf{fma}\left(-1, y \cdot \left(b \cdot y4 - i \cdot y5\right), y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y2 around inf

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}\right) \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot \color{blue}{y5}\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

      4. lift-*.f64 26.7

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - \color{blue}{y0 \cdot y5}\right)\right) \]

   7. Applied rewrites 26.7%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}\right) \]

   8. Taylor expanded in y0 around inf

      \[\leadsto k \cdot \left(y2 \cdot \left(-1 \cdot \left(y0 \cdot \color{blue}{y5}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(-1 \cdot \left(y0 \cdot y5\right)\right)\right) \]

      2. lift-*.f64 17.1

         \[\leadsto k \cdot \left(y2 \cdot \left(-1 \cdot \left(y0 \cdot y5\right)\right)\right) \]

   10. Applied rewrites 17.1%

       \[\leadsto k \cdot \left(y2 \cdot \left(-1 \cdot \left(y0 \cdot \color{blue}{y5}\right)\right)\right) \]

   if 8.39999999999999966e-190 < j < 2.55000000000000002e-89

   1. Initial program 35.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 35.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

      5. lower-*.f64 26.5

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   7. Applied rewrites 26.5%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 18.3

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]

   10. Applied rewrites 18.3%

       \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]

   if 2.55000000000000002e-89 < j < 4.2e101

   1. Initial program 32.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 25.3

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 25.3%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto b \cdot \left(a \cdot \left(x \cdot \color{blue}{y}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(a \cdot \left(x \cdot y\right)\right) \]

      2. lift-*.f64 17.9

         \[\leadsto b \cdot \left(a \cdot \left(x \cdot y\right)\right) \]

   10. Applied rewrites 17.9%

       \[\leadsto b \cdot \left(a \cdot \left(x \cdot \color{blue}{y}\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 30: 22.5% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right)\\ \mathbf{if}\;j \leq -8.4 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-251}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+231}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (* -1.0 (* j y0))))))
   (if (<= j -8.4e+102)
     t_1
     (if (<= j -2.2e-251)
       (* y4 (* c (* y y3)))
       (if (<= j 3.5e+53)
         (* a (* y3 (* -1.0 (* y y5))))
         (if (<= j 1.48e+231) (* y4 (* -1.0 (* y3 (* j y1)))) 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 * (x * (-1.0 * (j * y0)));
	double tmp;
	if (j <= -8.4e+102) {
		tmp = t_1;
	} else if (j <= -2.2e-251) {
		tmp = y4 * (c * (y * y3));
	} else if (j <= 3.5e+53) {
		tmp = a * (y3 * (-1.0 * (y * y5)));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	} 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 * (x * ((-1.0d0) * (j * y0)))
    if (j <= (-8.4d+102)) then
        tmp = t_1
    else if (j <= (-2.2d-251)) then
        tmp = y4 * (c * (y * y3))
    else if (j <= 3.5d+53) then
        tmp = a * (y3 * ((-1.0d0) * (y * y5)))
    else if (j <= 1.48d+231) then
        tmp = y4 * ((-1.0d0) * (y3 * (j * y1)))
    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 * (x * (-1.0 * (j * y0)));
	double tmp;
	if (j <= -8.4e+102) {
		tmp = t_1;
	} else if (j <= -2.2e-251) {
		tmp = y4 * (c * (y * y3));
	} else if (j <= 3.5e+53) {
		tmp = a * (y3 * (-1.0 * (y * y5)));
	} else if (j <= 1.48e+231) {
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	} 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 * (x * (-1.0 * (j * y0)))
	tmp = 0
	if j <= -8.4e+102:
		tmp = t_1
	elif j <= -2.2e-251:
		tmp = y4 * (c * (y * y3))
	elif j <= 3.5e+53:
		tmp = a * (y3 * (-1.0 * (y * y5)))
	elif j <= 1.48e+231:
		tmp = y4 * (-1.0 * (y3 * (j * y1)))
	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(x * Float64(-1.0 * Float64(j * y0))))
	tmp = 0.0
	if (j <= -8.4e+102)
		tmp = t_1;
	elseif (j <= -2.2e-251)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (j <= 3.5e+53)
		tmp = Float64(a * Float64(y3 * Float64(-1.0 * Float64(y * y5))));
	elseif (j <= 1.48e+231)
		tmp = Float64(y4 * Float64(-1.0 * Float64(y3 * Float64(j * y1))));
	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 * (x * (-1.0 * (j * y0)));
	tmp = 0.0;
	if (j <= -8.4e+102)
		tmp = t_1;
	elseif (j <= -2.2e-251)
		tmp = y4 * (c * (y * y3));
	elseif (j <= 3.5e+53)
		tmp = a * (y3 * (-1.0 * (y * y5)));
	elseif (j <= 1.48e+231)
		tmp = y4 * (-1.0 * (y3 * (j * y1)));
	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[(x * N[(-1.0 * N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.4e+102], t$95$1, If[LessEqual[j, -2.2e-251], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e+53], N[(a * N[(y3 * N[(-1.0 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.48e+231], N[(y4 * N[(-1.0 * N[(y3 * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -8.40000000000000006e102 or 1.47999999999999997e231 < j

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 37.0%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 36.2

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 36.2%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

      2. lift-*.f64 32.8

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

   10. Applied rewrites 32.8%

       \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]

   if -8.40000000000000006e102 < j < -2.2e-251

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 37.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y1 - c \cdot y\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - \color{blue}{c \cdot y}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot \color{blue}{y}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 22.7

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 22.7%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) \]

      2. lower-*.f64 17.2

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) \]

   10. Applied rewrites 17.2%

       \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) \]

   if -2.2e-251 < j < 3.50000000000000019e53

   1. Initial program 34.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 34.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

      5. lower-*.f64 26.0

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot \color{blue}{y5}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right)\right)\right) \]

      2. lift-*.f64 15.7

         \[\leadsto a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right)\right)\right) \]

   10. Applied rewrites 15.7%

       \[\leadsto a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot \color{blue}{y5}\right)\right)\right) \]

   if 3.50000000000000019e53 < j < 1.47999999999999997e231

   1. Initial program 27.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

   4. Applied rewrites 37.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y1 - c \cdot y\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - \color{blue}{c \cdot y}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot \color{blue}{y}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 31.4

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 31.4%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 25.5

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]

   10. Applied rewrites 25.5%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1\right)\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 31: 22.3% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right)\\ \mathbf{if}\;j \leq -8.4 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-187}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 2.55 \cdot 10^{-89}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+101}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (* -1.0 (* j y0))))))
   (if (<= j -8.4e+102)
     t_1
     (if (<= j 2.5e-187)
       (* y4 (* c (* y y3)))
       (if (<= j 2.55e-89)
         (* a (* y3 (* y1 z)))
         (if (<= j 4.2e+101) (* b (* a (* x y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * (-1.0 * (j * y0)));
	double tmp;
	if (j <= -8.4e+102) {
		tmp = t_1;
	} else if (j <= 2.5e-187) {
		tmp = y4 * (c * (y * y3));
	} else if (j <= 2.55e-89) {
		tmp = a * (y3 * (y1 * z));
	} else if (j <= 4.2e+101) {
		tmp = b * (a * (x * y));
	} 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 * (x * ((-1.0d0) * (j * y0)))
    if (j <= (-8.4d+102)) then
        tmp = t_1
    else if (j <= 2.5d-187) then
        tmp = y4 * (c * (y * y3))
    else if (j <= 2.55d-89) then
        tmp = a * (y3 * (y1 * z))
    else if (j <= 4.2d+101) then
        tmp = b * (a * (x * y))
    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 * (x * (-1.0 * (j * y0)));
	double tmp;
	if (j <= -8.4e+102) {
		tmp = t_1;
	} else if (j <= 2.5e-187) {
		tmp = y4 * (c * (y * y3));
	} else if (j <= 2.55e-89) {
		tmp = a * (y3 * (y1 * z));
	} else if (j <= 4.2e+101) {
		tmp = b * (a * (x * y));
	} 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 * (x * (-1.0 * (j * y0)))
	tmp = 0
	if j <= -8.4e+102:
		tmp = t_1
	elif j <= 2.5e-187:
		tmp = y4 * (c * (y * y3))
	elif j <= 2.55e-89:
		tmp = a * (y3 * (y1 * z))
	elif j <= 4.2e+101:
		tmp = b * (a * (x * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(x * Float64(-1.0 * Float64(j * y0))))
	tmp = 0.0
	if (j <= -8.4e+102)
		tmp = t_1;
	elseif (j <= 2.5e-187)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (j <= 2.55e-89)
		tmp = Float64(a * Float64(y3 * Float64(y1 * z)));
	elseif (j <= 4.2e+101)
		tmp = Float64(b * Float64(a * Float64(x * y)));
	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 * (x * (-1.0 * (j * y0)));
	tmp = 0.0;
	if (j <= -8.4e+102)
		tmp = t_1;
	elseif (j <= 2.5e-187)
		tmp = y4 * (c * (y * y3));
	elseif (j <= 2.55e-89)
		tmp = a * (y3 * (y1 * z));
	elseif (j <= 4.2e+101)
		tmp = b * (a * (x * y));
	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[(x * N[(-1.0 * N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.4e+102], t$95$1, If[LessEqual[j, 2.5e-187], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.55e-89], N[(a * N[(y3 * N[(y1 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.2e+101], N[(b * N[(a * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -8.40000000000000006e102 or 4.2e101 < j

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 35.6

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 35.6%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

      2. lift-*.f64 31.1

         \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot y0\right)\right)\right) \]

   10. Applied rewrites 31.1%

       \[\leadsto b \cdot \left(x \cdot \left(-1 \cdot \left(j \cdot \color{blue}{y0}\right)\right)\right) \]

   if -8.40000000000000006e102 < j < 2.4999999999999998e-187

   1. Initial program 33.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

   4. Applied rewrites 37.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y1 - c \cdot y\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - \color{blue}{c \cdot y}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot \color{blue}{y}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 21.8

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 21.8%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) \]

      2. lower-*.f64 17.7

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) \]

   10. Applied rewrites 17.7%

       \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) \]

   if 2.4999999999999998e-187 < j < 2.55000000000000002e-89

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 35.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

      5. lower-*.f64 27.0

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   7. Applied rewrites 27.0%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 18.6

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]

   10. Applied rewrites 18.6%

       \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]

   if 2.55000000000000002e-89 < j < 4.2e101

   1. Initial program 32.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 25.3

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 25.3%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto b \cdot \left(a \cdot \left(x \cdot \color{blue}{y}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(a \cdot \left(x \cdot y\right)\right) \]

      2. lift-*.f64 17.9

         \[\leadsto b \cdot \left(a \cdot \left(x \cdot y\right)\right) \]

   10. Applied rewrites 17.9%

       \[\leadsto b \cdot \left(a \cdot \left(x \cdot \color{blue}{y}\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 32: 22.2% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(x \cdot \left(a \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 26500000000000:\\ \;\;\;\;b \cdot \left(-1 \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -3.25e+67)
   (* b (* x (* a y)))
   (if (<= y 26500000000000.0)
     (* b (* -1.0 (* j (* x y0))))
     (* y4 (* c (* y y3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -3.25e+67) {
		tmp = b * (x * (a * y));
	} else if (y <= 26500000000000.0) {
		tmp = b * (-1.0 * (j * (x * y0)));
	} else {
		tmp = y4 * (c * (y * y3));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-3.25d+67)) then
        tmp = b * (x * (a * y))
    else if (y <= 26500000000000.0d0) then
        tmp = b * ((-1.0d0) * (j * (x * y0)))
    else
        tmp = y4 * (c * (y * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -3.25e+67) {
		tmp = b * (x * (a * y));
	} else if (y <= 26500000000000.0) {
		tmp = b * (-1.0 * (j * (x * y0)));
	} else {
		tmp = y4 * (c * (y * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -3.25e+67:
		tmp = b * (x * (a * y))
	elif y <= 26500000000000.0:
		tmp = b * (-1.0 * (j * (x * y0)))
	else:
		tmp = y4 * (c * (y * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -3.25e+67)
		tmp = Float64(b * Float64(x * Float64(a * y)));
	elseif (y <= 26500000000000.0)
		tmp = Float64(b * Float64(-1.0 * Float64(j * Float64(x * y0))));
	else
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -3.25e+67)
		tmp = b * (x * (a * y));
	elseif (y <= 26500000000000.0)
		tmp = b * (-1.0 * (j * (x * y0)));
	else
		tmp = y4 * (c * (y * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -3.25e+67], N[(b * N[(x * N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 26500000000000.0], N[(b * N[(-1.0 * N[(j * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2499999999999998e67

   1. Initial program 23.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 35.4

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 35.4%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto b \cdot \left(x \cdot \left(a \cdot y\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 30.3

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y\right)\right) \]

   10. Applied rewrites 30.3%

       \[\leadsto b \cdot \left(x \cdot \left(a \cdot y\right)\right) \]

   if -3.2499999999999998e67 < y < 2.65e13

   1. Initial program 34.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 37.1%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 21.1

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 21.1%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(-1 \cdot \left(j \cdot \color{blue}{\left(x \cdot y0\right)}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(j \cdot \left(x \cdot \color{blue}{y0}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right) \]

      3. lower-*.f64 17.7

         \[\leadsto b \cdot \left(-1 \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right) \]

   10. Applied rewrites 17.7%

       \[\leadsto b \cdot \left(-1 \cdot \left(j \cdot \color{blue}{\left(x \cdot y0\right)}\right)\right) \]

   if 2.65e13 < y

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y1 - c \cdot y\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - \color{blue}{c \cdot y}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot \color{blue}{y}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 32.4

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 32.4%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) \]

      2. lower-*.f64 26.6

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) \]

   10. Applied rewrites 26.6%

       \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 33: 22.1% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -5 \cdot 10^{+74}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.22 \cdot 10^{+39}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -5e+74)
   (* k (* y2 (* y1 y4)))
   (if (<= y1 1.22e+39) (* y4 (* c (* y y3))) (* a (* z (* y1 y3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -5e+74) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y1 <= 1.22e+39) {
		tmp = y4 * (c * (y * y3));
	} else {
		tmp = a * (z * (y1 * y3));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-5d+74)) then
        tmp = k * (y2 * (y1 * y4))
    else if (y1 <= 1.22d+39) then
        tmp = y4 * (c * (y * y3))
    else
        tmp = a * (z * (y1 * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -5e+74) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y1 <= 1.22e+39) {
		tmp = y4 * (c * (y * y3));
	} else {
		tmp = a * (z * (y1 * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -5e+74:
		tmp = k * (y2 * (y1 * y4))
	elif y1 <= 1.22e+39:
		tmp = y4 * (c * (y * y3))
	else:
		tmp = a * (z * (y1 * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -5e+74)
		tmp = Float64(k * Float64(y2 * Float64(y1 * y4)));
	elseif (y1 <= 1.22e+39)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	else
		tmp = Float64(a * Float64(z * Float64(y1 * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -5e+74)
		tmp = k * (y2 * (y1 * y4));
	elseif (y1 <= 1.22e+39)
		tmp = y4 * (c * (y * y3));
	else
		tmp = a * (z * (y1 * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -5e+74], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.22e+39], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -4.99999999999999963e74

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{-1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

   4. Applied rewrites 35.6%

      \[\leadsto \color{blue}{k \cdot \left(\mathsf{fma}\left(-1, y \cdot \left(b \cdot y4 - i \cdot y5\right), y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y2 around inf

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}\right) \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot \color{blue}{y5}\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

      4. lift-*.f64 33.9

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - \color{blue}{y0 \cdot y5}\right)\right) \]

   7. Applied rewrites 33.9%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}\right) \]

   8. Taylor expanded in y0 around 0

      \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 29.7

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right) \]

   10. Applied rewrites 29.7%

       \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right) \]

   if -4.99999999999999963e74 < y1 < 1.22e39

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

   4. Applied rewrites 35.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y1 - c \cdot y\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - \color{blue}{c \cdot y}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot \color{blue}{y}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

      5. lower-*.f64 21.2

         \[\leadsto y4 \cdot \left(-1 \cdot \left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]

   7. Applied rewrites 21.2%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot y1 - c \cdot y\right)\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) \]

      2. lower-*.f64 17.6

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) \]

   10. Applied rewrites 17.6%

       \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) \]

   if 1.22e39 < y1

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 38.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + \color{blue}{y1 \cdot y3}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot \color{blue}{t}, y1 \cdot y3\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

      5. lower-*.f64 35.2

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

   7. Applied rewrites 35.2%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right)} \]

   8. Taylor expanded in t around 0

      \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 29.4

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right) \]

   10. Applied rewrites 29.4%

       \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 34: 22.0% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -3 \cdot 10^{+67}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.15 \cdot 10^{-52}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -3e+67)
   (* k (* y2 (* y1 y4)))
   (if (<= y1 1.15e-52) (* b (* a (* x y))) (* a (* z (* y1 y3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -3e+67) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y1 <= 1.15e-52) {
		tmp = b * (a * (x * y));
	} else {
		tmp = a * (z * (y1 * y3));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-3d+67)) then
        tmp = k * (y2 * (y1 * y4))
    else if (y1 <= 1.15d-52) then
        tmp = b * (a * (x * y))
    else
        tmp = a * (z * (y1 * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -3e+67) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y1 <= 1.15e-52) {
		tmp = b * (a * (x * y));
	} else {
		tmp = a * (z * (y1 * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -3e+67:
		tmp = k * (y2 * (y1 * y4))
	elif y1 <= 1.15e-52:
		tmp = b * (a * (x * y))
	else:
		tmp = a * (z * (y1 * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -3e+67)
		tmp = Float64(k * Float64(y2 * Float64(y1 * y4)));
	elseif (y1 <= 1.15e-52)
		tmp = Float64(b * Float64(a * Float64(x * y)));
	else
		tmp = Float64(a * Float64(z * Float64(y1 * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -3e+67)
		tmp = k * (y2 * (y1 * y4));
	elseif (y1 <= 1.15e-52)
		tmp = b * (a * (x * y));
	else
		tmp = a * (z * (y1 * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -3e+67], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.15e-52], N[(b * N[(a * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -3.0000000000000001e67

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{-1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

   4. Applied rewrites 35.6%

      \[\leadsto \color{blue}{k \cdot \left(\mathsf{fma}\left(-1, y \cdot \left(b \cdot y4 - i \cdot y5\right), y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y2 around inf

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}\right) \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot \color{blue}{y5}\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

      4. lift-*.f64 33.7

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - \color{blue}{y0 \cdot y5}\right)\right) \]

   7. Applied rewrites 33.7%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}\right) \]

   8. Taylor expanded in y0 around 0

      \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 29.4

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right) \]

   10. Applied rewrites 29.4%

       \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right) \]

   if -3.0000000000000001e67 < y1 < 1.14999999999999997e-52

   1. Initial program 34.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 38.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 28.7

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 28.7%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto b \cdot \left(a \cdot \left(x \cdot \color{blue}{y}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(a \cdot \left(x \cdot y\right)\right) \]

      2. lift-*.f64 18.0

         \[\leadsto b \cdot \left(a \cdot \left(x \cdot y\right)\right) \]

   10. Applied rewrites 18.0%

       \[\leadsto b \cdot \left(a \cdot \left(x \cdot \color{blue}{y}\right)\right) \]

   if 1.14999999999999997e-52 < y1

   1. Initial program 25.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 38.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + \color{blue}{y1 \cdot y3}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot \color{blue}{t}, y1 \cdot y3\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

      5. lower-*.f64 32.2

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

   7. Applied rewrites 32.2%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right)} \]

   8. Taylor expanded in t around 0

      \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 25.5

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right) \]

   10. Applied rewrites 25.5%

       \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 35: 22.0% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+159}:\\ \;\;\;\;b \cdot \left(x \cdot \left(a \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-25}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -6.4e+159)
   (* b (* x (* a y)))
   (if (<= y 2e-25) (* a (* y3 (* y1 z))) (* b (* a (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -6.4e+159) {
		tmp = b * (x * (a * y));
	} else if (y <= 2e-25) {
		tmp = a * (y3 * (y1 * z));
	} else {
		tmp = b * (a * (x * y));
	}
	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 (y <= (-6.4d+159)) then
        tmp = b * (x * (a * y))
    else if (y <= 2d-25) then
        tmp = a * (y3 * (y1 * z))
    else
        tmp = b * (a * (x * y))
    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 (y <= -6.4e+159) {
		tmp = b * (x * (a * y));
	} else if (y <= 2e-25) {
		tmp = a * (y3 * (y1 * z));
	} else {
		tmp = b * (a * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -6.4e+159:
		tmp = b * (x * (a * y))
	elif y <= 2e-25:
		tmp = a * (y3 * (y1 * z))
	else:
		tmp = b * (a * (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -6.4e+159)
		tmp = Float64(b * Float64(x * Float64(a * y)));
	elseif (y <= 2e-25)
		tmp = Float64(a * Float64(y3 * Float64(y1 * z)));
	else
		tmp = Float64(b * Float64(a * Float64(x * y)));
	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 (y <= -6.4e+159)
		tmp = b * (x * (a * y));
	elseif (y <= 2e-25)
		tmp = a * (y3 * (y1 * z));
	else
		tmp = b * (a * (x * y));
	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[y, -6.4e+159], N[(b * N[(x * N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-25], N[(a * N[(y3 * N[(y1 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.3999999999999997e159

   1. Initial program 21.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 37.4

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 37.4%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto b \cdot \left(x \cdot \left(a \cdot y\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 33.6

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y\right)\right) \]

   10. Applied rewrites 33.6%

       \[\leadsto b \cdot \left(x \cdot \left(a \cdot y\right)\right) \]

   if -6.3999999999999997e159 < y < 2.00000000000000008e-25

   1. Initial program 34.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 36.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

      5. lower-*.f64 22.3

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   7. Applied rewrites 22.3%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 17.8

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]

   10. Applied rewrites 17.8%

       \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]

   if 2.00000000000000008e-25 < y

   1. Initial program 24.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.1%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 31.8

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 31.8%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto b \cdot \left(a \cdot \left(x \cdot \color{blue}{y}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(a \cdot \left(x \cdot y\right)\right) \]

      2. lift-*.f64 26.8

         \[\leadsto b \cdot \left(a \cdot \left(x \cdot y\right)\right) \]

   10. Applied rewrites 26.8%

       \[\leadsto b \cdot \left(a \cdot \left(x \cdot \color{blue}{y}\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 36: 21.7% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-25}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* a (* x y)))))
   (if (<= y -6.4e+159) t_1 (if (<= y 2e-25) (* a (* y3 (* y1 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 * (a * (x * y));
	double tmp;
	if (y <= -6.4e+159) {
		tmp = t_1;
	} else if (y <= 2e-25) {
		tmp = a * (y3 * (y1 * 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 * (a * (x * y))
    if (y <= (-6.4d+159)) then
        tmp = t_1
    else if (y <= 2d-25) then
        tmp = a * (y3 * (y1 * 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 * (a * (x * y));
	double tmp;
	if (y <= -6.4e+159) {
		tmp = t_1;
	} else if (y <= 2e-25) {
		tmp = a * (y3 * (y1 * 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 * (a * (x * y))
	tmp = 0
	if y <= -6.4e+159:
		tmp = t_1
	elif y <= 2e-25:
		tmp = a * (y3 * (y1 * 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(a * Float64(x * y)))
	tmp = 0.0
	if (y <= -6.4e+159)
		tmp = t_1;
	elseif (y <= 2e-25)
		tmp = Float64(a * Float64(y3 * Float64(y1 * 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 * (a * (x * y));
	tmp = 0.0;
	if (y <= -6.4e+159)
		tmp = t_1;
	elseif (y <= 2e-25)
		tmp = a * (y3 * (y1 * 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[(a * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+159], t$95$1, If[LessEqual[y, 2e-25], N[(a * N[(y3 * N[(y1 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.3999999999999997e159 or 2.00000000000000008e-25 < y

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.2%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 33.6

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 33.6%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto b \cdot \left(a \cdot \left(x \cdot \color{blue}{y}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(a \cdot \left(x \cdot y\right)\right) \]

      2. lift-*.f64 28.7

         \[\leadsto b \cdot \left(a \cdot \left(x \cdot y\right)\right) \]

   10. Applied rewrites 28.7%

       \[\leadsto b \cdot \left(a \cdot \left(x \cdot \color{blue}{y}\right)\right) \]

   if -6.3999999999999997e159 < y < 2.00000000000000008e-25

   1. Initial program 34.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in 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 36.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

      5. lower-*.f64 22.3

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   7. Applied rewrites 22.3%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 17.8

         \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]

   10. Applied rewrites 17.8%

       \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 37: 17.7% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* z (* y1 y3))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (z * (y1 * y3));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (z * (y1 * y3))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (z * (y1 * y3));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (z * (y1 * y3))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(z * Float64(y1 * y3)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (z * (y1 * y3));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 30.0%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

2. Taylor expanded in z around -inf

   \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

   3. lower--.f64 N/A

      \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

4. Applied rewrites 36.8%

   \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

5. Taylor expanded in a around -inf

   \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
6. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)}\right) \]

   2. lower-*.f64 N/A

      \[\leadsto a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + \color{blue}{y1 \cdot y3}\right)\right) \]

   3. lower-fma.f64 N/A

      \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot \color{blue}{t}, y1 \cdot y3\right)\right) \]

   4. lower-*.f64 N/A

      \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

   5. lower-*.f64 27.2

      \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

7. Applied rewrites 27.2%

   \[\leadsto a \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right)} \]

8. Taylor expanded in t around 0

   \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right) \]
9. Step-by-step derivation

   1. lift-*.f64 17.7

      \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right) \]

10. Applied rewrites 17.7%

    \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right) \]
11. Add Preprocessing

Alternative 38: 17.6% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y3 (* y1 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) {
	return a * (y3 * (y1 * z));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y3 * (y1 * z))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y3 * (y1 * z));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y3 * (y1 * z))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y3 * Float64(y1 * z)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y3 * (y1 * z));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y3 * N[(y1 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 30.0%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

2. Taylor expanded in 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 36.9%

   \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

5. Taylor expanded in a around -inf

   \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
6. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

   2. lower-*.f64 N/A

      \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - \color{blue}{y \cdot y5}\right)\right) \]

   3. lower--.f64 N/A

      \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot \color{blue}{y5}\right)\right) \]

   4. lower-*.f64 N/A

      \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

   5. lower-*.f64 26.4

      \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right) \]

7. Applied rewrites 26.4%

   \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

8. Taylor expanded in y around 0

   \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]
9. Step-by-step derivation

   1. lift-*.f64 17.6

      \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]

10. Applied rewrites 17.6%

    \[\leadsto a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right) \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025114 
(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)))))