Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.3% → 53.6%

Time: 20.5s

Alternatives: 44

Speedup: 4.4×

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

Specification

Math

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

FPCore

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

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]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	(((((((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 code

Initial Program: 29.3% accurate, 1.0× speedup

Math

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

FPCore

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

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]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	(((((((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 code

Alternative 1: 53.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

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 = ((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0));
	double t_2 = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + t_1;
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + 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 = ((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0))
	t_2 = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + t_1
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0)))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(y0 * b) - Float64(y1 * i)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(y0 * c) - Float64(y1 * a)))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * Float64(Float64(y4 * b) - Float64(y5 * i)))) - Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(y4 * c) - Float64(y5 * a)))) + t_1)
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * Float64(a * Float64(Float64(b * x) - Float64(y3 * y5)))) + 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 = ((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0));
	t_2 = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + t_1;
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(N[(y * N[(a * N[(N[(b * x), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $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 29.3%

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

   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 29.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 36.4%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 37.7%

      \[\leadsto y \cdot \left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 48.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} t_1 := \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ t_2 := y1 \cdot y4 - y0 \cdot y5\\ t_3 := c \cdot y0 - a \cdot y1\\ t_4 := c \cdot y4 - a \cdot y5\\ \mathbf{if}\;c \leq -2.031575241137308 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right) + t\_1\\ \mathbf{elif}\;c \leq -1.1610322526979148 \cdot 10^{-100}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(k, t\_2, x \cdot t\_3\right) - t \cdot t\_4\right)\\ \mathbf{elif}\;c \leq 111552693309562320:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(-1, a \cdot z, j \cdot y4\right)\right) + t\_1\\ \mathbf{elif}\;c \leq 3.3006743108811484 \cdot 10^{+108}:\\ \;\;\;\;-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, t\_2, z \cdot t\_3\right) - y \cdot t\_4\right)\right)\\ \mathbf{elif}\;c \leq 1.0676515338509748 \cdot 10^{+180}:\\ \;\;\;\;-1 \cdot \left(y3 \cdot \left(y0 \cdot \mathsf{fma}\left(-1, \frac{c \cdot \left(y \cdot y4\right)}{y0}, c \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\mathsf{fma}\left(-1, i \cdot \left(x \cdot y - t \cdot z\right), x \cdot \left(y0 \cdot y2\right)\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))
       (t_2 (- (* y1 y4) (* y0 y5)))
       (t_3 (- (* c y0) (* a y1)))
       (t_4 (- (* c y4) (* a y5))))
  (if (<= c -2.031575241137308e+37)
    (+ (* y (* -1.0 (* c (- (* i x) (* y3 y4))))) t_1)
    (if (<= c -1.1610322526979148e-100)
      (* y2 (- (fma k t_2 (* x t_3)) (* t t_4)))
      (if (<= c 111552693309562320.0)
        (+ (* b (* t (fma -1.0 (* a z) (* j y4)))) t_1)
        (if (<= c 3.3006743108811484e+108)
          (* -1.0 (* y3 (- (fma j t_2 (* z t_3)) (* y t_4))))
          (if (<= c 1.0676515338509748e+180)
            (*
             -1.0
             (* y3 (* y0 (fma -1.0 (/ (* c (* y y4)) y0) (* c z)))))
            (*
             c
             (-
              (fma -1.0 (* i (- (* x y) (* t z))) (* x (* y0 y2)))
              (* t (* y2 y4)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0));
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = (c * y0) - (a * y1);
	double t_4 = (c * y4) - (a * y5);
	double tmp;
	if (c <= -2.031575241137308e+37) {
		tmp = (y * (-1.0 * (c * ((i * x) - (y3 * y4))))) + t_1;
	} else if (c <= -1.1610322526979148e-100) {
		tmp = y2 * (fma(k, t_2, (x * t_3)) - (t * t_4));
	} else if (c <= 111552693309562320.0) {
		tmp = (b * (t * fma(-1.0, (a * z), (j * y4)))) + t_1;
	} else if (c <= 3.3006743108811484e+108) {
		tmp = -1.0 * (y3 * (fma(j, t_2, (z * t_3)) - (y * t_4)));
	} else if (c <= 1.0676515338509748e+180) {
		tmp = -1.0 * (y3 * (y0 * fma(-1.0, ((c * (y * y4)) / y0), (c * z))));
	} else {
		tmp = c * (fma(-1.0, (i * ((x * y) - (t * z))), (x * (y0 * y2))) - (t * (y2 * y4)));
	}
	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(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0)))
	t_2 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	t_4 = Float64(Float64(c * y4) - Float64(a * y5))
	tmp = 0.0
	if (c <= -2.031575241137308e+37)
		tmp = Float64(Float64(y * Float64(-1.0 * Float64(c * Float64(Float64(i * x) - Float64(y3 * y4))))) + t_1);
	elseif (c <= -1.1610322526979148e-100)
		tmp = Float64(y2 * Float64(fma(k, t_2, Float64(x * t_3)) - Float64(t * t_4)));
	elseif (c <= 111552693309562320.0)
		tmp = Float64(Float64(b * Float64(t * fma(-1.0, Float64(a * z), Float64(j * y4)))) + t_1);
	elseif (c <= 3.3006743108811484e+108)
		tmp = Float64(-1.0 * Float64(y3 * Float64(fma(j, t_2, Float64(z * t_3)) - Float64(y * t_4))));
	elseif (c <= 1.0676515338509748e+180)
		tmp = Float64(-1.0 * Float64(y3 * Float64(y0 * fma(-1.0, Float64(Float64(c * Float64(y * y4)) / y0), Float64(c * z)))));
	else
		tmp = Float64(c * Float64(fma(-1.0, Float64(i * Float64(Float64(x * y) - Float64(t * z))), Float64(x * Float64(y0 * y2))) - Float64(t * Float64(y2 * y4))));
	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[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.031575241137308e+37], N[(N[(y * N[(-1.0 * N[(c * N[(N[(i * x), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[c, -1.1610322526979148e-100], N[(y2 * N[(N[(k * t$95$2 + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(t * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 111552693309562320.0], N[(N[(b * N[(t * N[(-1.0 * N[(a * z), $MachinePrecision] + N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[c, 3.3006743108811484e+108], N[(-1.0 * N[(y3 * N[(N[(j * t$95$2 + N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.0676515338509748e+180], N[(-1.0 * N[(y3 * N[(y0 * N[(-1.0 * N[(N[(c * N[(y * y4), $MachinePrecision]), $MachinePrecision] / y0), $MachinePrecision] + N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(-1.0 * N[(i * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0))) IN
		LET t_2 = ((y1 * y4) - (y0 * y5)) IN
			LET t_3 = ((c * y0) - (a * y1)) IN
				LET t_4 = ((c * y4) - (a * y5)) IN
					LET tmp_4 = IF (c <= (1067651533850974763058200073262580337234119629367277878889823702291761479832326077814657915346339769843280021859942540800622559039414087383423284076296092161431525268471088249044992)) THEN ((-1) * (y3 * (y0 * (((-1) * ((c * (y * y4)) / y0)) + (c * z))))) ELSE (c * ((((-1) * (i * ((x * y) - (t * z)))) + (x * (y0 * y2))) - (t * (y2 * y4)))) ENDIF IN
					LET tmp_3 = IF (c <= (3300674310881148435117356897217906087455033817148960515614383853928178395698327689826923369805425048348000256)) THEN ((-1) * (y3 * (((j * t_2) + (z * t_3)) - (y * t_4)))) ELSE tmp_4 ENDIF IN
					LET tmp_2 = IF (c <= (111552693309562320)) THEN ((b * (t * (((-1) * (a * z)) + (j * y4)))) + t_1) ELSE tmp_3 ENDIF IN
					LET tmp_1 = IF (c <= (-1161032252697914806234328909934237643134118304034100497272017699523670768272207037643252840010158406968735031361727017693760347807028596242872923114304062861539677695406053229985319047440923875542337396918743110704675672244528180339463716073782062476738019540789537131786346435546875e-382)) THEN (y2 * (((k * t_2) + (x * t_3)) - (t * t_4))) ELSE tmp_2 ENDIF IN
					LET tmp = IF (c <= (-20315752411373078824712748265113649152)) THEN ((y * ((-1) * (c * ((i * x) - (y3 * y4))))) + t_1) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 6 regimes

2. if c < -2.0315752411373079e37

   1. Initial program 29.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 36.4%

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

   5. Taylor expanded in c around -inf

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

   7. Applied rewrites 38.6%

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

   if -2.0315752411373079e37 < c < -1.1610322526979148e-100

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   if -1.1610322526979148e-100 < c < 111552693309562320

   1. Initial program 29.3%

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

   2. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 35.8%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 37.7%

      \[\leadsto b \cdot \left(t \cdot \mathsf{fma}\left(-1, a \cdot z, j \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if 111552693309562320 < c < 3.3006743108811484e108

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   if 3.3006743108811484e108 < c < 1.0676515338509748e180

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in c around inf

      \[\leadsto -1 \cdot \left(y3 \cdot \left(c \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.1%

      \[\leadsto -1 \cdot \left(y3 \cdot \left(c \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right) \]

   8. Taylor expanded in y0 around inf

      \[\leadsto -1 \cdot \left(y3 \cdot \left(y0 \cdot \left(-1 \cdot \frac{c \cdot \left(y \cdot y4\right)}{y0} + c \cdot z\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 25.5%

       \[\leadsto -1 \cdot \left(y3 \cdot \left(y0 \cdot \mathsf{fma}\left(-1, \frac{c \cdot \left(y \cdot y4\right)}{y0}, c \cdot z\right)\right)\right) \]

   if 1.0676515338509748e180 < c

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in c around inf

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

   7. Applied rewrites 34.3%

      \[\leadsto c \cdot \left(\mathsf{fma}\left(-1, i \cdot \left(x \cdot y - t \cdot z\right), x \cdot \left(y0 \cdot y2\right)\right) - t \cdot \left(y2 \cdot y4\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 3: 40.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := t\_1 \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ t_3 := x \cdot y2 - y3 \cdot z\\ t_4 := x \cdot y - t \cdot z\\ t_5 := j \cdot x - k \cdot z\\ \mathbf{if}\;c \leq -436019.7310683261:\\ \;\;\;\;y \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right) + t\_2\\ \mathbf{elif}\;c \leq -3.456632376141069 \cdot 10^{-269}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b - c \cdot i, t\_4, \left(b \cdot y4 - i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot t\_5\\ \mathbf{elif}\;c \leq 3.3375929405650238 \cdot 10^{-90}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(-1, a \cdot z, j \cdot y4\right)\right) + t\_2\\ \mathbf{elif}\;c \leq 5.2944489674836265 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(\mathsf{fma}\left(-1, y1 \cdot t\_3, b \cdot t\_4\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(\mathsf{fma}\left(-1, a \cdot t\_3, y4 \cdot t\_1\right) - -1 \cdot \left(i \cdot t\_5\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- (* k y2) (* j y3)))
       (t_2 (* t_1 (- (* y4 y1) (* y5 y0))))
       (t_3 (- (* x y2) (* y3 z)))
       (t_4 (- (* x y) (* t z)))
       (t_5 (- (* j x) (* k z))))
  (if (<= c -436019.7310683261)
    (+ (* y (* -1.0 (* c (- (* i x) (* y3 y4))))) t_2)
    (if (<= c -3.456632376141069e-269)
      (-
       (fma
        (- (* a b) (* c i))
        t_4
        (* (- (* b y4) (* i y5)) (- (* j t) (* k y))))
       (* (- (* b y0) (* i y1)) t_5))
      (if (<= c 3.3375929405650238e-90)
        (+ (* b (* t (fma -1.0 (* a z) (* j y4)))) t_2)
        (if (<= c 5.2944489674836265e+113)
          (+
           (*
            a
            (-
             (fma -1.0 (* y1 t_3) (* b t_4))
             (* -1.0 (* y5 (- (* t y2) (* y y3))))))
           t_2)
          (*
           y1
           (-
            (fma -1.0 (* a t_3) (* y4 t_1))
            (* -1.0 (* i 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 = t_1 * ((y4 * y1) - (y5 * y0));
	double t_3 = (x * y2) - (y3 * z);
	double t_4 = (x * y) - (t * z);
	double t_5 = (j * x) - (k * z);
	double tmp;
	if (c <= -436019.7310683261) {
		tmp = (y * (-1.0 * (c * ((i * x) - (y3 * y4))))) + t_2;
	} else if (c <= -3.456632376141069e-269) {
		tmp = fma(((a * b) - (c * i)), t_4, (((b * y4) - (i * y5)) * ((j * t) - (k * y)))) - (((b * y0) - (i * y1)) * t_5);
	} else if (c <= 3.3375929405650238e-90) {
		tmp = (b * (t * fma(-1.0, (a * z), (j * y4)))) + t_2;
	} else if (c <= 5.2944489674836265e+113) {
		tmp = (a * (fma(-1.0, (y1 * t_3), (b * t_4)) - (-1.0 * (y5 * ((t * y2) - (y * y3)))))) + t_2;
	} else {
		tmp = y1 * (fma(-1.0, (a * t_3), (y4 * t_1)) - (-1.0 * (i * 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(t_1 * Float64(Float64(y4 * y1) - Float64(y5 * y0)))
	t_3 = Float64(Float64(x * y2) - Float64(y3 * z))
	t_4 = Float64(Float64(x * y) - Float64(t * z))
	t_5 = Float64(Float64(j * x) - Float64(k * z))
	tmp = 0.0
	if (c <= -436019.7310683261)
		tmp = Float64(Float64(y * Float64(-1.0 * Float64(c * Float64(Float64(i * x) - Float64(y3 * y4))))) + t_2);
	elseif (c <= -3.456632376141069e-269)
		tmp = Float64(fma(Float64(Float64(a * b) - Float64(c * i)), t_4, Float64(Float64(Float64(b * y4) - Float64(i * y5)) * Float64(Float64(j * t) - Float64(k * y)))) - Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_5));
	elseif (c <= 3.3375929405650238e-90)
		tmp = Float64(Float64(b * Float64(t * fma(-1.0, Float64(a * z), Float64(j * y4)))) + t_2);
	elseif (c <= 5.2944489674836265e+113)
		tmp = Float64(Float64(a * Float64(fma(-1.0, Float64(y1 * t_3), Float64(b * t_4)) - Float64(-1.0 * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))))) + t_2);
	else
		tmp = Float64(y1 * Float64(fma(-1.0, Float64(a * t_3), Float64(y4 * t_1)) - Float64(-1.0 * Float64(i * 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[(t$95$1 * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -436019.7310683261], N[(N[(y * N[(-1.0 * N[(c * N[(N[(i * x), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[c, -3.456632376141069e-269], N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * t$95$4 + N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.3375929405650238e-90], N[(N[(b * N[(t * N[(-1.0 * N[(a * z), $MachinePrecision] + N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[c, 5.2944489674836265e+113], N[(N[(a * N[(N[(-1.0 * N[(y1 * t$95$3), $MachinePrecision] + N[(b * t$95$4), $MachinePrecision]), $MachinePrecision] - N[(-1.0 * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(y1 * N[(N[(-1.0 * N[(a * t$95$3), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(-1.0 * N[(i * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = ((k * y2) - (j * y3)) IN
		LET t_2 = (t_1 * ((y4 * y1) - (y5 * y0))) IN
			LET t_3 = ((x * y2) - (y3 * z)) IN
				LET t_4 = ((x * y) - (t * z)) IN
					LET t_5 = ((j * x) - (k * z)) IN
						LET tmp_3 = IF (c <= (529444896748362646033002980965557427081248487504395761327005319526392495533152046901616620824934219297969066213376)) THEN ((a * ((((-1) * (y1 * t_3)) + (b * t_4)) - ((-1) * (y5 * ((t * y2) - (y * y3)))))) + t_2) ELSE (y1 * ((((-1) * (a * t_3)) + (y4 * t_1)) - ((-1) * (i * t_5)))) ENDIF IN
						LET tmp_2 = IF (c <= (333759294056502376051933313400403725082174206844735461851942285299363419791429914910460165299665976820470555963857096593203047004789257791826762627609895058136370319931615929138065468749863226225126152161261899071551385691225544150029236334376037120819091796875e-350)) THEN ((b * (t * (((-1) * (a * z)) + (j * y4)))) + t_2) ELSE tmp_3 ENDIF IN
						LET tmp_1 = IF (c <= (-345663237614106913460890894969157737796823686840535136075179756070720937805193553967667413197181733044085868135628440000649062017953613660912438550887405788952717176345022262794404343248696690604597273604382582836739820047324861812661959021213313489944657351740583417675188178831147249516835579168220383523160731255848936107293115688919285204204920129006989666391707222759140334950253420065328244279826645273711495338548142358589912413625580987786736388147867356987189144828459888071046147397017062884541196710452968869272294205086938981945515169081647954851014795778976900617200851957340976436200054848277309343884088724627497919467296327855621029812027700245380401611328125e-943)) THEN (((((a * b) - (c * i)) * t_4) + (((b * y4) - (i * y5)) * ((j * t) - (k * y)))) - (((b * y0) - (i * y1)) * t_5)) ELSE tmp_2 ENDIF IN
						LET tmp = IF (c <= (-4360197310683261021040380001068115234375e-34)) THEN ((y * ((-1) * (c * ((i * x) - (y3 * y4))))) + t_2) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if c < -436019.7310683261

   1. Initial program 29.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 36.4%

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

   5. Taylor expanded in c around -inf

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

   7. Applied rewrites 38.6%

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

   if -436019.7310683261 < c < -3.4566323761410691e-269

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in y2 around 0

      \[\leadsto \left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 38.3%

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

   if -3.4566323761410691e-269 < c < 3.3375929405650238e-90

   1. Initial program 29.3%

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

   2. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 35.8%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 37.7%

      \[\leadsto b \cdot \left(t \cdot \mathsf{fma}\left(-1, a \cdot z, j \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if 3.3375929405650238e-90 < c < 5.2944489674836265e113

   1. Initial program 29.3%

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

   2. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.3%

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

   if 5.2944489674836265e113 < c

   1. Initial program 29.3%

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

   2. Taylor expanded in y1 around inf

      \[\leadsto y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.0%

      \[\leadsto y1 \cdot \left(\mathsf{fma}\left(-1, a \cdot \left(x \cdot y2 - y3 \cdot z\right), y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 40.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := t\_1 \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ t_3 := j \cdot x - k \cdot z\\ \mathbf{if}\;c \leq -436019.7310683261:\\ \;\;\;\;y \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right) + t\_2\\ \mathbf{elif}\;c \leq -3.456632376141069 \cdot 10^{-269}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b - c \cdot i, x \cdot y - t \cdot z, \left(b \cdot y4 - i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot t\_3\\ \mathbf{elif}\;c \leq 111552693309562320:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(-1, a \cdot z, j \cdot y4\right)\right) + t\_2\\ \mathbf{elif}\;c \leq 4.393048225754463 \cdot 10^{+115}:\\ \;\;\;\;-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(\mathsf{fma}\left(-1, a \cdot \left(x \cdot y2 - y3 \cdot z\right), y4 \cdot t\_1\right) - -1 \cdot \left(i \cdot t\_3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- (* k y2) (* j y3)))
       (t_2 (* t_1 (- (* y4 y1) (* y5 y0))))
       (t_3 (- (* j x) (* k z))))
  (if (<= c -436019.7310683261)
    (+ (* y (* -1.0 (* c (- (* i x) (* y3 y4))))) t_2)
    (if (<= c -3.456632376141069e-269)
      (-
       (fma
        (- (* a b) (* c i))
        (- (* x y) (* t z))
        (* (- (* b y4) (* i y5)) (- (* j t) (* k y))))
       (* (- (* b y0) (* i y1)) t_3))
      (if (<= c 111552693309562320.0)
        (+ (* b (* t (fma -1.0 (* a z) (* j y4)))) t_2)
        (if (<= c 4.393048225754463e+115)
          (*
           -1.0
           (*
            y3
            (-
             (fma
              j
              (- (* y1 y4) (* y0 y5))
              (* z (- (* c y0) (* a y1))))
             (* y (- (* c y4) (* a y5))))))
          (*
           y1
           (-
            (fma -1.0 (* a (- (* x y2) (* y3 z))) (* y4 t_1))
            (* -1.0 (* i 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 = t_1 * ((y4 * y1) - (y5 * y0));
	double t_3 = (j * x) - (k * z);
	double tmp;
	if (c <= -436019.7310683261) {
		tmp = (y * (-1.0 * (c * ((i * x) - (y3 * y4))))) + t_2;
	} else if (c <= -3.456632376141069e-269) {
		tmp = fma(((a * b) - (c * i)), ((x * y) - (t * z)), (((b * y4) - (i * y5)) * ((j * t) - (k * y)))) - (((b * y0) - (i * y1)) * t_3);
	} else if (c <= 111552693309562320.0) {
		tmp = (b * (t * fma(-1.0, (a * z), (j * y4)))) + t_2;
	} else if (c <= 4.393048225754463e+115) {
		tmp = -1.0 * (y3 * (fma(j, ((y1 * y4) - (y0 * y5)), (z * ((c * y0) - (a * y1)))) - (y * ((c * y4) - (a * y5)))));
	} else {
		tmp = y1 * (fma(-1.0, (a * ((x * y2) - (y3 * z))), (y4 * t_1)) - (-1.0 * (i * 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(t_1 * Float64(Float64(y4 * y1) - Float64(y5 * y0)))
	t_3 = Float64(Float64(j * x) - Float64(k * z))
	tmp = 0.0
	if (c <= -436019.7310683261)
		tmp = Float64(Float64(y * Float64(-1.0 * Float64(c * Float64(Float64(i * x) - Float64(y3 * y4))))) + t_2);
	elseif (c <= -3.456632376141069e-269)
		tmp = Float64(fma(Float64(Float64(a * b) - Float64(c * i)), Float64(Float64(x * y) - Float64(t * z)), Float64(Float64(Float64(b * y4) - Float64(i * y5)) * Float64(Float64(j * t) - Float64(k * y)))) - Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_3));
	elseif (c <= 111552693309562320.0)
		tmp = Float64(Float64(b * Float64(t * fma(-1.0, Float64(a * z), Float64(j * y4)))) + t_2);
	elseif (c <= 4.393048225754463e+115)
		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 = Float64(y1 * Float64(fma(-1.0, Float64(a * Float64(Float64(x * y2) - Float64(y3 * z))), Float64(y4 * t_1)) - Float64(-1.0 * Float64(i * 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[(t$95$1 * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -436019.7310683261], N[(N[(y * N[(-1.0 * N[(c * N[(N[(i * x), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[c, -3.456632376141069e-269], N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 111552693309562320.0], N[(N[(b * N[(t * N[(-1.0 * N[(a * z), $MachinePrecision] + N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[c, 4.393048225754463e+115], 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], N[(y1 * N[(N[(-1.0 * N[(a * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(-1.0 * N[(i * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = ((k * y2) - (j * y3)) IN
		LET t_2 = (t_1 * ((y4 * y1) - (y5 * y0))) IN
			LET t_3 = ((j * x) - (k * z)) IN
				LET tmp_3 = IF (c <= (43930482257544627543507866707220576510262198581452622990275719605903074213086823929503177602542296471207194363166720)) THEN ((-1) * (y3 * (((j * ((y1 * y4) - (y0 * y5))) + (z * ((c * y0) - (a * y1)))) - (y * ((c * y4) - (a * y5)))))) ELSE (y1 * ((((-1) * (a * ((x * y2) - (y3 * z)))) + (y4 * t_1)) - ((-1) * (i * t_3)))) ENDIF IN
				LET tmp_2 = IF (c <= (111552693309562320)) THEN ((b * (t * (((-1) * (a * z)) + (j * y4)))) + t_2) ELSE tmp_3 ENDIF IN
				LET tmp_1 = IF (c <= (-345663237614106913460890894969157737796823686840535136075179756070720937805193553967667413197181733044085868135628440000649062017953613660912438550887405788952717176345022262794404343248696690604597273604382582836739820047324861812661959021213313489944657351740583417675188178831147249516835579168220383523160731255848936107293115688919285204204920129006989666391707222759140334950253420065328244279826645273711495338548142358589912413625580987786736388147867356987189144828459888071046147397017062884541196710452968869272294205086938981945515169081647954851014795778976900617200851957340976436200054848277309343884088724627497919467296327855621029812027700245380401611328125e-943)) THEN (((((a * b) - (c * i)) * ((x * y) - (t * z))) + (((b * y4) - (i * y5)) * ((j * t) - (k * y)))) - (((b * y0) - (i * y1)) * t_3)) ELSE tmp_2 ENDIF IN
				LET tmp = IF (c <= (-4360197310683261021040380001068115234375e-34)) THEN ((y * ((-1) * (c * ((i * x) - (y3 * y4))))) + t_2) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if c < -436019.7310683261

   1. Initial program 29.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 36.4%

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

   5. Taylor expanded in c around -inf

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

   7. Applied rewrites 38.6%

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

   if -436019.7310683261 < c < -3.4566323761410691e-269

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in y2 around 0

      \[\leadsto \left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 38.3%

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

   if -3.4566323761410691e-269 < c < 111552693309562320

   1. Initial program 29.3%

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

   2. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 35.8%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 37.7%

      \[\leadsto b \cdot \left(t \cdot \mathsf{fma}\left(-1, a \cdot z, j \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if 111552693309562320 < c < 4.3930482257544628e115

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   if 4.3930482257544628e115 < c

   1. Initial program 29.3%

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

   2. Taylor expanded in y1 around inf

      \[\leadsto y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.0%

      \[\leadsto y1 \cdot \left(\mathsf{fma}\left(-1, a \cdot \left(x \cdot y2 - y3 \cdot z\right), y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 5: 40.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := t\_1 \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := c \cdot y0 - a \cdot y1\\ t_5 := c \cdot y4 - a \cdot y5\\ \mathbf{if}\;c \leq -2.031575241137308 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right) + t\_2\\ \mathbf{elif}\;c \leq -1.1610322526979148 \cdot 10^{-100}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(k, t\_3, x \cdot t\_4\right) - t \cdot t\_5\right)\\ \mathbf{elif}\;c \leq 111552693309562320:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(-1, a \cdot z, j \cdot y4\right)\right) + t\_2\\ \mathbf{elif}\;c \leq 4.393048225754463 \cdot 10^{+115}:\\ \;\;\;\;-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, t\_3, z \cdot t\_4\right) - y \cdot t\_5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(\mathsf{fma}\left(-1, a \cdot \left(x \cdot y2 - y3 \cdot z\right), y4 \cdot t\_1\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- (* k y2) (* j y3)))
       (t_2 (* t_1 (- (* y4 y1) (* y5 y0))))
       (t_3 (- (* y1 y4) (* y0 y5)))
       (t_4 (- (* c y0) (* a y1)))
       (t_5 (- (* c y4) (* a y5))))
  (if (<= c -2.031575241137308e+37)
    (+ (* y (* -1.0 (* c (- (* i x) (* y3 y4))))) t_2)
    (if (<= c -1.1610322526979148e-100)
      (* y2 (- (fma k t_3 (* x t_4)) (* t t_5)))
      (if (<= c 111552693309562320.0)
        (+ (* b (* t (fma -1.0 (* a z) (* j y4)))) t_2)
        (if (<= c 4.393048225754463e+115)
          (* -1.0 (* y3 (- (fma j t_3 (* z t_4)) (* y t_5))))
          (*
           y1
           (-
            (fma -1.0 (* a (- (* x y2) (* y3 z))) (* y4 t_1))
            (* -1.0 (* i (- (* j x) (* k z))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = t_1 * ((y4 * y1) - (y5 * y0));
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (c * y4) - (a * y5);
	double tmp;
	if (c <= -2.031575241137308e+37) {
		tmp = (y * (-1.0 * (c * ((i * x) - (y3 * y4))))) + t_2;
	} else if (c <= -1.1610322526979148e-100) {
		tmp = y2 * (fma(k, t_3, (x * t_4)) - (t * t_5));
	} else if (c <= 111552693309562320.0) {
		tmp = (b * (t * fma(-1.0, (a * z), (j * y4)))) + t_2;
	} else if (c <= 4.393048225754463e+115) {
		tmp = -1.0 * (y3 * (fma(j, t_3, (z * t_4)) - (y * t_5)));
	} else {
		tmp = y1 * (fma(-1.0, (a * ((x * y2) - (y3 * z))), (y4 * t_1)) - (-1.0 * (i * ((j * x) - (k * z)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(t_1 * Float64(Float64(y4 * y1) - Float64(y5 * y0)))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	t_5 = Float64(Float64(c * y4) - Float64(a * y5))
	tmp = 0.0
	if (c <= -2.031575241137308e+37)
		tmp = Float64(Float64(y * Float64(-1.0 * Float64(c * Float64(Float64(i * x) - Float64(y3 * y4))))) + t_2);
	elseif (c <= -1.1610322526979148e-100)
		tmp = Float64(y2 * Float64(fma(k, t_3, Float64(x * t_4)) - Float64(t * t_5)));
	elseif (c <= 111552693309562320.0)
		tmp = Float64(Float64(b * Float64(t * fma(-1.0, Float64(a * z), Float64(j * y4)))) + t_2);
	elseif (c <= 4.393048225754463e+115)
		tmp = Float64(-1.0 * Float64(y3 * Float64(fma(j, t_3, Float64(z * t_4)) - Float64(y * t_5))));
	else
		tmp = Float64(y1 * Float64(fma(-1.0, Float64(a * Float64(Float64(x * y2) - Float64(y3 * z))), Float64(y4 * t_1)) - Float64(-1.0 * Float64(i * Float64(Float64(j * x) - Float64(k * z))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.031575241137308e+37], N[(N[(y * N[(-1.0 * N[(c * N[(N[(i * x), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[c, -1.1610322526979148e-100], N[(y2 * N[(N[(k * t$95$3 + N[(x * t$95$4), $MachinePrecision]), $MachinePrecision] - N[(t * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 111552693309562320.0], N[(N[(b * N[(t * N[(-1.0 * N[(a * z), $MachinePrecision] + N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[c, 4.393048225754463e+115], N[(-1.0 * N[(y3 * N[(N[(j * t$95$3 + N[(z * t$95$4), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(N[(-1.0 * N[(a * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(-1.0 * N[(i * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = ((k * y2) - (j * y3)) IN
		LET t_2 = (t_1 * ((y4 * y1) - (y5 * y0))) IN
			LET t_3 = ((y1 * y4) - (y0 * y5)) IN
				LET t_4 = ((c * y0) - (a * y1)) IN
					LET t_5 = ((c * y4) - (a * y5)) IN
						LET tmp_3 = IF (c <= (43930482257544627543507866707220576510262198581452622990275719605903074213086823929503177602542296471207194363166720)) THEN ((-1) * (y3 * (((j * t_3) + (z * t_4)) - (y * t_5)))) ELSE (y1 * ((((-1) * (a * ((x * y2) - (y3 * z)))) + (y4 * t_1)) - ((-1) * (i * ((j * x) - (k * z)))))) ENDIF IN
						LET tmp_2 = IF (c <= (111552693309562320)) THEN ((b * (t * (((-1) * (a * z)) + (j * y4)))) + t_2) ELSE tmp_3 ENDIF IN
						LET tmp_1 = IF (c <= (-1161032252697914806234328909934237643134118304034100497272017699523670768272207037643252840010158406968735031361727017693760347807028596242872923114304062861539677695406053229985319047440923875542337396918743110704675672244528180339463716073782062476738019540789537131786346435546875e-382)) THEN (y2 * (((k * t_3) + (x * t_4)) - (t * t_5))) ELSE tmp_2 ENDIF IN
						LET tmp = IF (c <= (-20315752411373078824712748265113649152)) THEN ((y * ((-1) * (c * ((i * x) - (y3 * y4))))) + t_2) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if c < -2.0315752411373079e37

   1. Initial program 29.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 36.4%

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

   5. Taylor expanded in c around -inf

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

   7. Applied rewrites 38.6%

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

   if -2.0315752411373079e37 < c < -1.1610322526979148e-100

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   if -1.1610322526979148e-100 < c < 111552693309562320

   1. Initial program 29.3%

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

   2. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 35.8%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 37.7%

      \[\leadsto b \cdot \left(t \cdot \mathsf{fma}\left(-1, a \cdot z, j \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if 111552693309562320 < c < 4.3930482257544628e115

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   if 4.3930482257544628e115 < c

   1. Initial program 29.3%

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

   2. Taylor expanded in y1 around inf

      \[\leadsto y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.0%

      \[\leadsto y1 \cdot \left(\mathsf{fma}\left(-1, a \cdot \left(x \cdot y2 - y3 \cdot z\right), y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 6: 39.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a))))
       (t_2 (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a))))
       (t_3 (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i))))
       (t_4 (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))
  (if (<=
       (+
        (-
         (+
          (+
           (-
            (* (- (* x y) (* z t)) (- (* a b) (* c i)))
            (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i))))
           t_1)
          t_3)
         t_2)
        t_4)
       INFINITY)
    (+
     (-
      (+ (+ (* -1.0 (* j (* x (- (* b y0) (* i y1))))) t_1) t_3)
      t_2)
     t_4)
    (+ (* y (* a (- (* b x) (* y3 y5)))) t_4))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a));
	double t_2 = ((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a));
	double t_3 = ((t * j) - (y * k)) * ((y4 * b) - (y5 * i));
	double t_4 = ((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0));
	double tmp;
	if (((((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + t_1) + t_3) - t_2) + t_4) <= ((double) INFINITY)) {
		tmp = ((((-1.0 * (j * (x * ((b * y0) - (i * y1))))) + t_1) + t_3) - t_2) + t_4;
	} else {
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + t_4;
	}
	return tmp;
}

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 = ((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a));
	double t_2 = ((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a));
	double t_3 = ((t * j) - (y * k)) * ((y4 * b) - (y5 * i));
	double t_4 = ((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0));
	double tmp;
	if (((((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + t_1) + t_3) - t_2) + t_4) <= Double.POSITIVE_INFINITY) {
		tmp = ((((-1.0 * (j * (x * ((b * y0) - (i * y1))))) + t_1) + t_3) - t_2) + t_4;
	} else {
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = ((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a))
	t_2 = ((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a))
	t_3 = ((t * j) - (y * k)) * ((y4 * b) - (y5 * i))
	t_4 = ((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0))
	tmp = 0
	if ((((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + t_1) + t_3) - t_2) + t_4) <= math.inf:
		tmp = ((((-1.0 * (j * (x * ((b * y0) - (i * y1))))) + t_1) + t_3) - t_2) + t_4
	else:
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(y0 * c) - Float64(y1 * a)))
	t_2 = Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(y4 * c) - Float64(y5 * a)))
	t_3 = Float64(Float64(Float64(t * j) - Float64(y * k)) * Float64(Float64(y4 * b) - Float64(y5 * i)))
	t_4 = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0)))
	tmp = 0.0
	if (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)))) + t_1) + t_3) - t_2) + t_4) <= Inf)
		tmp = Float64(Float64(Float64(Float64(Float64(-1.0 * Float64(j * Float64(x * Float64(Float64(b * y0) - Float64(i * y1))))) + t_1) + t_3) - t_2) + t_4);
	else
		tmp = Float64(Float64(y * Float64(a * Float64(Float64(b * x) - Float64(y3 * y5)))) + t_4);
	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 = ((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a));
	t_2 = ((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a));
	t_3 = ((t * j) - (y * k)) * ((y4 * b) - (y5 * i));
	t_4 = ((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0));
	tmp = 0.0;
	if (((((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + t_1) + t_3) - t_2) + t_4) <= Inf)
		tmp = ((((-1.0 * (j * (x * ((b * y0) - (i * y1))))) + t_1) + t_3) - t_2) + t_4;
	else
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[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] + t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision] - t$95$2), $MachinePrecision] + t$95$4), $MachinePrecision], Infinity], N[(N[(N[(N[(N[(-1.0 * N[(j * N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision] - t$95$2), $MachinePrecision] + t$95$4), $MachinePrecision], N[(N[(y * N[(a * N[(N[(b * x), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $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 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 31.6%

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

   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 29.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 36.4%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 37.7%

      \[\leadsto y \cdot \left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 38.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \mathbf{if}\;b \leq -2.0093261147099653 \cdot 10^{+222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3261417219797.4985:\\ \;\;\;\;a \cdot \left(\mathsf{fma}\left(-1, x \cdot \left(y1 \cdot y2\right), b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.4642740575504475 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;b \leq 0.00039011209874830117:\\ \;\;\;\;j \cdot \left(y5 \cdot \mathsf{fma}\left(-1, i \cdot t, y0 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1
        (-
         (* b (* y4 (- (* j t) (* k y))))
         (* b (* y0 (- (* j x) (* k z)))))))
  (if (<= b -2.0093261147099653e+222)
    t_1
    (if (<= b -3261417219797.4985)
      (*
       a
       (-
        (fma -1.0 (* x (* y1 y2)) (* b (- (* x y) (* t z))))
        (* -1.0 (* t (* y2 y5)))))
      (if (<= b 1.4642740575504475e-122)
        (+
         (* y (* a (- (* b x) (* y3 y5))))
         (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))
        (if (<= b 0.00039011209874830117)
          (* j (* y5 (fma -1.0 (* i t) (* y0 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 * (y4 * ((j * t) - (k * y)))) - (b * (y0 * ((j * x) - (k * z))));
	double tmp;
	if (b <= -2.0093261147099653e+222) {
		tmp = t_1;
	} else if (b <= -3261417219797.4985) {
		tmp = a * (fma(-1.0, (x * (y1 * y2)), (b * ((x * y) - (t * z)))) - (-1.0 * (t * (y2 * y5))));
	} else if (b <= 1.4642740575504475e-122) {
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
	} else if (b <= 0.00039011209874830117) {
		tmp = j * (y5 * fma(-1.0, (i * t), (y0 * 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(Float64(b * Float64(y4 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(b * Float64(y0 * Float64(Float64(j * x) - Float64(k * z)))))
	tmp = 0.0
	if (b <= -2.0093261147099653e+222)
		tmp = t_1;
	elseif (b <= -3261417219797.4985)
		tmp = Float64(a * Float64(fma(-1.0, Float64(x * Float64(y1 * y2)), Float64(b * Float64(Float64(x * y) - Float64(t * z)))) - Float64(-1.0 * Float64(t * Float64(y2 * y5)))));
	elseif (b <= 1.4642740575504475e-122)
		tmp = Float64(Float64(y * Float64(a * Float64(Float64(b * x) - Float64(y3 * y5)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	elseif (b <= 0.00039011209874830117)
		tmp = Float64(j * Float64(y5 * fma(-1.0, Float64(i * t), Float64(y0 * y3))));
	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[(N[(b * N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y0 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.0093261147099653e+222], t$95$1, If[LessEqual[b, -3261417219797.4985], N[(a * N[(N[(-1.0 * N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1.0 * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4642740575504475e-122], N[(N[(y * N[(a * N[(N[(b * x), $MachinePrecision] - N[(y3 * y5), $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[b, 0.00039011209874830117], N[(j * N[(y5 * N[(-1.0 * N[(i * t), $MachinePrecision] + N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = ((b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * ((j * x) - (k * z))))) IN
		LET tmp_3 = IF (b <= (39011209874830117018407182882810957380570471286773681640625e-62)) THEN (j * (y5 * (((-1) * (i * t)) + (y0 * y3)))) ELSE t_1 ENDIF IN
		LET tmp_2 = IF (b <= (146427405755044751147982395051639959133404390898501830564528192167109684721259404454734592459065694181917762201755093016950750439790739402407991860692669151158228971462936604692528663233849684947975966915975674460345111845400991981712628371527042529433882695942803795434975850420753077903165766636417455259788766852580010890960693359375e-457)) THEN ((y * (a * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (b <= (-326141721979749853515625e-11)) THEN (a * ((((-1) * (x * (y1 * y2))) + (b * ((x * y) - (t * z)))) - ((-1) * (t * (y2 * y5))))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (b <= (-2009326114709965263420526121308186879752816103802638840710871457261942856615427714468646967878974968965502725571576674584102989091233508205957588300657262363003876344379852954346113011250913423345682272823886788249887178752)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if b < -2.0093261147099653e222 or 3.9011209874830117e-4 < b

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in y2 around 0

      \[\leadsto \left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 38.3%

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

   8. Taylor expanded in i around 0

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

   10. Applied rewrites 31.6%

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

   11. Taylor expanded in a around 0

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 32.2%

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   if -2.0093261147099653e222 < b < -3261417219797.4985

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(x \cdot \left(y1 \cdot y2\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto a \cdot \left(\mathsf{fma}\left(-1, x \cdot \left(y1 \cdot y2\right), b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]

   if -3261417219797.4985 < b < 1.4642740575504475e-122

   1. Initial program 29.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 36.4%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 37.7%

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

   if 1.4642740575504475e-122 < b < 3.9011209874830117e-4

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in j around -inf

      \[\leadsto j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.5%

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

Alternative 8: 38.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} t_1 := \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{if}\;c \leq -2.031575241137308 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right) + t\_1\\ \mathbf{elif}\;c \leq -1.1610322526979148 \cdot 10^{-100}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq 1.9309591853508485 \cdot 10^{+195}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(-1, a \cdot z, j \cdot y4\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\mathsf{fma}\left(-1, i \cdot \left(x \cdot y - t \cdot z\right), x \cdot \left(y0 \cdot y2\right)\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))
  (if (<= c -2.031575241137308e+37)
    (+ (* y (* -1.0 (* c (- (* i x) (* y3 y4))))) t_1)
    (if (<= c -1.1610322526979148e-100)
      (*
       y2
       (-
        (fma k (- (* y1 y4) (* y0 y5)) (* x (- (* c y0) (* a y1))))
        (* t (- (* c y4) (* a y5)))))
      (if (<= c 1.9309591853508485e+195)
        (+ (* b (* t (fma -1.0 (* a z) (* j y4)))) t_1)
        (*
         c
         (-
          (fma -1.0 (* i (- (* x y) (* t z))) (* x (* y0 y2)))
          (* t (* y2 y4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0));
	double tmp;
	if (c <= -2.031575241137308e+37) {
		tmp = (y * (-1.0 * (c * ((i * x) - (y3 * y4))))) + t_1;
	} else if (c <= -1.1610322526979148e-100) {
		tmp = y2 * (fma(k, ((y1 * y4) - (y0 * y5)), (x * ((c * y0) - (a * y1)))) - (t * ((c * y4) - (a * y5))));
	} else if (c <= 1.9309591853508485e+195) {
		tmp = (b * (t * fma(-1.0, (a * z), (j * y4)))) + t_1;
	} else {
		tmp = c * (fma(-1.0, (i * ((x * y) - (t * z))), (x * (y0 * y2))) - (t * (y2 * y4)));
	}
	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(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0)))
	tmp = 0.0
	if (c <= -2.031575241137308e+37)
		tmp = Float64(Float64(y * Float64(-1.0 * Float64(c * Float64(Float64(i * x) - Float64(y3 * y4))))) + t_1);
	elseif (c <= -1.1610322526979148e-100)
		tmp = Float64(y2 * Float64(fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) - Float64(t * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (c <= 1.9309591853508485e+195)
		tmp = Float64(Float64(b * Float64(t * fma(-1.0, Float64(a * z), Float64(j * y4)))) + t_1);
	else
		tmp = Float64(c * Float64(fma(-1.0, Float64(i * Float64(Float64(x * y) - Float64(t * z))), Float64(x * Float64(y0 * y2))) - Float64(t * Float64(y2 * y4))));
	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[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.031575241137308e+37], N[(N[(y * N[(-1.0 * N[(c * N[(N[(i * x), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[c, -1.1610322526979148e-100], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.9309591853508485e+195], N[(N[(b * N[(t * N[(-1.0 * N[(a * z), $MachinePrecision] + N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(c * N[(N[(-1.0 * N[(i * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0))) IN
		LET tmp_2 = IF (c <= (1930959185350848519945197651311780208397114449998164520358447316939698934888588389915998066808036075276943366538915496296189581702574152111281165005793763952382359749559771993535814863576075599872)) THEN ((b * (t * (((-1) * (a * z)) + (j * y4)))) + t_1) ELSE (c * ((((-1) * (i * ((x * y) - (t * z)))) + (x * (y0 * y2))) - (t * (y2 * y4)))) ENDIF IN
		LET tmp_1 = IF (c <= (-1161032252697914806234328909934237643134118304034100497272017699523670768272207037643252840010158406968735031361727017693760347807028596242872923114304062861539677695406053229985319047440923875542337396918743110704675672244528180339463716073782062476738019540789537131786346435546875e-382)) THEN (y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) - (t * ((c * y4) - (a * y5))))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (c <= (-20315752411373078824712748265113649152)) THEN ((y * ((-1) * (c * ((i * x) - (y3 * y4))))) + t_1) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if c < -2.0315752411373079e37

   1. Initial program 29.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 36.4%

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

   5. Taylor expanded in c around -inf

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

   7. Applied rewrites 38.6%

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

   if -2.0315752411373079e37 < c < -1.1610322526979148e-100

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   if -1.1610322526979148e-100 < c < 1.9309591853508485e195

   1. Initial program 29.3%

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

   2. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 35.8%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 37.7%

      \[\leadsto b \cdot \left(t \cdot \mathsf{fma}\left(-1, a \cdot z, j \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if 1.9309591853508485e195 < c

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in c around inf

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

   7. Applied rewrites 34.3%

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

Alternative 9: 37.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \mathbf{if}\;b \leq -2.0093261147099653 \cdot 10^{+222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2190442247793.5693:\\ \;\;\;\;a \cdot \left(\mathsf{fma}\left(-1, x \cdot \left(y1 \cdot y2\right), b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.6914941165271957 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;b \leq 1096.8954990076757:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \mathsf{fma}\left(-1, c \cdot z, j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1
        (-
         (* b (* y4 (- (* j t) (* k y))))
         (* b (* y0 (- (* j x) (* k z)))))))
  (if (<= b -2.0093261147099653e+222)
    t_1
    (if (<= b -2190442247793.5693)
      (*
       a
       (-
        (fma -1.0 (* x (* y1 y2)) (* b (- (* x y) (* t z))))
        (* -1.0 (* t (* y2 y5)))))
      (if (<= b 2.6914941165271957e-161)
        (+
         (* a (* y (- (* b x) (* y3 y5))))
         (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))
        (if (<= b 1096.8954990076757)
          (* y0 (* y3 (fma -1.0 (* c z) (* j y5))))
          t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * ((j * x) - (k * z))));
	double tmp;
	if (b <= -2.0093261147099653e+222) {
		tmp = t_1;
	} else if (b <= -2190442247793.5693) {
		tmp = a * (fma(-1.0, (x * (y1 * y2)), (b * ((x * y) - (t * z)))) - (-1.0 * (t * (y2 * y5))));
	} else if (b <= 2.6914941165271957e-161) {
		tmp = (a * (y * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
	} else if (b <= 1096.8954990076757) {
		tmp = y0 * (y3 * fma(-1.0, (c * z), (j * y5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * Float64(y4 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(b * Float64(y0 * Float64(Float64(j * x) - Float64(k * z)))))
	tmp = 0.0
	if (b <= -2.0093261147099653e+222)
		tmp = t_1;
	elseif (b <= -2190442247793.5693)
		tmp = Float64(a * Float64(fma(-1.0, Float64(x * Float64(y1 * y2)), Float64(b * Float64(Float64(x * y) - Float64(t * z)))) - Float64(-1.0 * Float64(t * Float64(y2 * y5)))));
	elseif (b <= 2.6914941165271957e-161)
		tmp = Float64(Float64(a * Float64(y * Float64(Float64(b * x) - Float64(y3 * y5)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	elseif (b <= 1096.8954990076757)
		tmp = Float64(y0 * Float64(y3 * fma(-1.0, Float64(c * z), Float64(j * y5))));
	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[(N[(b * N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y0 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.0093261147099653e+222], t$95$1, If[LessEqual[b, -2190442247793.5693], N[(a * N[(N[(-1.0 * N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1.0 * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6914941165271957e-161], N[(N[(a * N[(y * N[(N[(b * x), $MachinePrecision] - N[(y3 * y5), $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[b, 1096.8954990076757], N[(y0 * N[(y3 * N[(-1.0 * N[(c * z), $MachinePrecision] + N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = ((b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * ((j * x) - (k * z))))) IN
		LET tmp_3 = IF (b <= (1096895499007675653047044761478900909423828125e-42)) THEN (y0 * (y3 * (((-1) * (c * z)) + (j * y5)))) ELSE t_1 ENDIF IN
		LET tmp_2 = IF (b <= (26914941165271957298177719226611762397572885881960157210074199329244939562035693432873432981858944897035832193039883459865820583201833414560309386945637109311276882323305985552023028985449115259480042828161321834056281105991514484887419415429417096592752109216651008062517440118527006188063515085345980496184591121357896133997210053838883202065013414831770840439948957406515420520231977874470175038368324749171733856201171875e-585)) THEN ((a * (y * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (b <= (-21904422477935693359375e-10)) THEN (a * ((((-1) * (x * (y1 * y2))) + (b * ((x * y) - (t * z)))) - ((-1) * (t * (y2 * y5))))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (b <= (-2009326114709965263420526121308186879752816103802638840710871457261942856615427714468646967878974968965502725571576674584102989091233508205957588300657262363003876344379852954346113011250913423345682272823886788249887178752)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if b < -2.0093261147099653e222 or 1096.8954990076757 < b

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in y2 around 0

      \[\leadsto \left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 38.3%

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

   8. Taylor expanded in i around 0

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

   10. Applied rewrites 31.6%

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

   11. Taylor expanded in a around 0

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 32.2%

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   if -2.0093261147099653e222 < b < -2190442247793.5693

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(x \cdot \left(y1 \cdot y2\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto a \cdot \left(\mathsf{fma}\left(-1, x \cdot \left(y1 \cdot y2\right), b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]

   if -2190442247793.5693 < b < 2.6914941165271957e-161

   1. Initial program 29.3%

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

   2. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.3%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 38.0%

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

   if 2.6914941165271957e-161 < b < 1096.8954990076757

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

Alternative 10: 37.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} t_1 := \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{if}\;c \leq -1.998074942438889 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right) + t\_1\\ \mathbf{elif}\;c \leq -1.1610322526979148 \cdot 10^{-100}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 1.9309591853508485 \cdot 10^{+195}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(-1, a \cdot z, j \cdot y4\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\mathsf{fma}\left(-1, i \cdot \left(x \cdot y - t \cdot z\right), x \cdot \left(y0 \cdot y2\right)\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))
  (if (<= c -1.998074942438889e+37)
    (+ (* y (* -1.0 (* c (- (* i x) (* y3 y4))))) t_1)
    (if (<= c -1.1610322526979148e-100)
      (*
       y2
       (fma k (- (* y1 y4) (* y0 y5)) (* x (- (* c y0) (* a y1)))))
      (if (<= c 1.9309591853508485e+195)
        (+ (* b (* t (fma -1.0 (* a z) (* j y4)))) t_1)
        (*
         c
         (-
          (fma -1.0 (* i (- (* x y) (* t z))) (* x (* y0 y2)))
          (* t (* y2 y4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0));
	double tmp;
	if (c <= -1.998074942438889e+37) {
		tmp = (y * (-1.0 * (c * ((i * x) - (y3 * y4))))) + t_1;
	} else if (c <= -1.1610322526979148e-100) {
		tmp = y2 * fma(k, ((y1 * y4) - (y0 * y5)), (x * ((c * y0) - (a * y1))));
	} else if (c <= 1.9309591853508485e+195) {
		tmp = (b * (t * fma(-1.0, (a * z), (j * y4)))) + t_1;
	} else {
		tmp = c * (fma(-1.0, (i * ((x * y) - (t * z))), (x * (y0 * y2))) - (t * (y2 * y4)));
	}
	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(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0)))
	tmp = 0.0
	if (c <= -1.998074942438889e+37)
		tmp = Float64(Float64(y * Float64(-1.0 * Float64(c * Float64(Float64(i * x) - Float64(y3 * y4))))) + t_1);
	elseif (c <= -1.1610322526979148e-100)
		tmp = Float64(y2 * fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))));
	elseif (c <= 1.9309591853508485e+195)
		tmp = Float64(Float64(b * Float64(t * fma(-1.0, Float64(a * z), Float64(j * y4)))) + t_1);
	else
		tmp = Float64(c * Float64(fma(-1.0, Float64(i * Float64(Float64(x * y) - Float64(t * z))), Float64(x * Float64(y0 * y2))) - Float64(t * Float64(y2 * y4))));
	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[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.998074942438889e+37], N[(N[(y * N[(-1.0 * N[(c * N[(N[(i * x), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[c, -1.1610322526979148e-100], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.9309591853508485e+195], N[(N[(b * N[(t * N[(-1.0 * N[(a * z), $MachinePrecision] + N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(c * N[(N[(-1.0 * N[(i * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0))) IN
		LET tmp_2 = IF (c <= (1930959185350848519945197651311780208397114449998164520358447316939698934888588389915998066808036075276943366538915496296189581702574152111281165005793763952382359749559771993535814863576075599872)) THEN ((b * (t * (((-1) * (a * z)) + (j * y4)))) + t_1) ELSE (c * ((((-1) * (i * ((x * y) - (t * z)))) + (x * (y0 * y2))) - (t * (y2 * y4)))) ENDIF IN
		LET tmp_1 = IF (c <= (-1161032252697914806234328909934237643134118304034100497272017699523670768272207037643252840010158406968735031361727017693760347807028596242872923114304062861539677695406053229985319047440923875542337396918743110704675672244528180339463716073782062476738019540789537131786346435546875e-382)) THEN (y2 * ((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1))))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (c <= (-19980749424388889381110125573926027264)) THEN ((y * ((-1) * (c * ((i * x) - (y3 * y4))))) + t_1) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if c < -1.9980749424388889e37

   1. Initial program 29.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 36.4%

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

   5. Taylor expanded in c around -inf

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

   7. Applied rewrites 38.6%

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

   if -1.9980749424388889e37 < c < -1.1610322526979148e-100

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

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

   if -1.1610322526979148e-100 < c < 1.9309591853508485e195

   1. Initial program 29.3%

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

   2. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 35.8%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 37.7%

      \[\leadsto b \cdot \left(t \cdot \mathsf{fma}\left(-1, a \cdot z, j \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if 1.9309591853508485e195 < c

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in c around inf

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

   7. Applied rewrites 34.3%

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

Alternative 11: 36.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \mathbf{if}\;b \leq -2.0093261147099653 \cdot 10^{+222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.278856606470336 \cdot 10^{-132}:\\ \;\;\;\;a \cdot \left(\mathsf{fma}\left(-1, x \cdot \left(y1 \cdot y2\right), b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right)\\ \mathbf{elif}\;b \leq -1.0592487913441096 \cdot 10^{-262}:\\ \;\;\;\;y \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right) + \left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{elif}\;b \leq 1.6115288797132272 \cdot 10^{-212}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 1096.8954990076757:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \mathsf{fma}\left(-1, c \cdot z, j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1
        (-
         (* b (* y4 (- (* j t) (* k y))))
         (* b (* y0 (- (* j x) (* k z)))))))
  (if (<= b -2.0093261147099653e+222)
    t_1
    (if (<= b -9.278856606470336e-132)
      (*
       a
       (-
        (fma -1.0 (* x (* y1 y2)) (* b (- (* x y) (* t z))))
        (* -1.0 (* t (* y2 y5)))))
      (if (<= b -1.0592487913441096e-262)
        (+
         (* y (* -1.0 (* c (- (* i x) (* y3 y4)))))
         (* (* k y2) (* y1 y4)))
        (if (<= b 1.6115288797132272e-212)
          (*
           y2
           (fma
            k
            (- (* y1 y4) (* y0 y5))
            (* x (- (* c y0) (* a y1)))))
          (if (<= b 1096.8954990076757)
            (* y0 (* y3 (fma -1.0 (* c z) (* j y5))))
            t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * ((j * x) - (k * z))));
	double tmp;
	if (b <= -2.0093261147099653e+222) {
		tmp = t_1;
	} else if (b <= -9.278856606470336e-132) {
		tmp = a * (fma(-1.0, (x * (y1 * y2)), (b * ((x * y) - (t * z)))) - (-1.0 * (t * (y2 * y5))));
	} else if (b <= -1.0592487913441096e-262) {
		tmp = (y * (-1.0 * (c * ((i * x) - (y3 * y4))))) + ((k * y2) * (y1 * y4));
	} else if (b <= 1.6115288797132272e-212) {
		tmp = y2 * fma(k, ((y1 * y4) - (y0 * y5)), (x * ((c * y0) - (a * y1))));
	} else if (b <= 1096.8954990076757) {
		tmp = y0 * (y3 * fma(-1.0, (c * z), (j * y5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * Float64(y4 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(b * Float64(y0 * Float64(Float64(j * x) - Float64(k * z)))))
	tmp = 0.0
	if (b <= -2.0093261147099653e+222)
		tmp = t_1;
	elseif (b <= -9.278856606470336e-132)
		tmp = Float64(a * Float64(fma(-1.0, Float64(x * Float64(y1 * y2)), Float64(b * Float64(Float64(x * y) - Float64(t * z)))) - Float64(-1.0 * Float64(t * Float64(y2 * y5)))));
	elseif (b <= -1.0592487913441096e-262)
		tmp = Float64(Float64(y * Float64(-1.0 * Float64(c * Float64(Float64(i * x) - Float64(y3 * y4))))) + Float64(Float64(k * y2) * Float64(y1 * y4)));
	elseif (b <= 1.6115288797132272e-212)
		tmp = Float64(y2 * fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))));
	elseif (b <= 1096.8954990076757)
		tmp = Float64(y0 * Float64(y3 * fma(-1.0, Float64(c * z), Float64(j * y5))));
	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[(N[(b * N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y0 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.0093261147099653e+222], t$95$1, If[LessEqual[b, -9.278856606470336e-132], N[(a * N[(N[(-1.0 * N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1.0 * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.0592487913441096e-262], N[(N[(y * N[(-1.0 * N[(c * N[(N[(i * x), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * y2), $MachinePrecision] * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6115288797132272e-212], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1096.8954990076757], N[(y0 * N[(y3 * N[(-1.0 * N[(c * z), $MachinePrecision] + N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = ((b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * ((j * x) - (k * z))))) IN
		LET tmp_4 = IF (b <= (1096895499007675653047044761478900909423828125e-42)) THEN (y0 * (y3 * (((-1) * (c * z)) + (j * y5)))) ELSE t_1 ENDIF IN
		LET tmp_3 = IF (b <= (1611528879713227174050611709674011657656107538605551913366296714592994601470065121364137184602953694863995276970269110631416915841532217873341354389215515582181351185707982512119417956580383981715201739216823125535028354083411396474067673207422685361717573717366712831401789262078057685613036272275617296696302496958406623811574964922193511244093281539082871147418479545677340833854354846475725668388209145095461379372844828710472112611959391701335593724804986569561707661223982821711131508168236649617376110565913904792978428304195404052734375e-755)) THEN (y2 * ((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1))))) ELSE tmp_4 ENDIF IN
		LET tmp_2 = IF (b <= (-10592487913441095702974115054631615741168692337999911171471786741640989785887393426615625450216774277353384664674349199155993247625317544835910074982034411475354659622212485640316091642908520726147664571597472397977105408252197532658159622614423513901443889654340373263159601667923152865158338655519326121516401330792505596417212514310307585151647205717423075305406697713836973774880073119713332101720125035561009234759753248915929631485691330485771123522608606722929146264828241008373633620062533026795847132066369764273241356753067275453876194927002963174367956428768861490734790367244107856500180051350122330802437414960792683160661908914335072040557861328125e-923)) THEN ((y * ((-1) * (c * ((i * x) - (y3 * y4))))) + ((k * y2) * (y1 * y4))) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (b <= (-927885660647033588836024719243981982345339155776047091567942997078063094533562011064640888073072791320884442125586198971997838514185929001488196304908613058044435952572183614373256613402741741017317847826826430701955444552566068396074812176857786923244216324806779678591664172137360983726296956928519473733242369406677696463958682215888984501361846923828125e-488)) THEN (a * ((((-1) * (x * (y1 * y2))) + (b * ((x * y) - (t * z)))) - ((-1) * (t * (y2 * y5))))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (b <= (-2009326114709965263420526121308186879752816103802638840710871457261942856615427714468646967878974968965502725571576674584102989091233508205957588300657262363003876344379852954346113011250913423345682272823886788249887178752)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if b < -2.0093261147099653e222 or 1096.8954990076757 < b

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in y2 around 0

      \[\leadsto \left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 38.3%

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

   8. Taylor expanded in i around 0

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

   10. Applied rewrites 31.6%

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

   11. Taylor expanded in a around 0

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 32.2%

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   if -2.0093261147099653e222 < b < -9.2788566064703359e-132

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(x \cdot \left(y1 \cdot y2\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto a \cdot \left(\mathsf{fma}\left(-1, x \cdot \left(y1 \cdot y2\right), b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]

   if -9.2788566064703359e-132 < b < -1.0592487913441096e-262

   1. Initial program 29.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 36.4%

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

   5. Taylor expanded in c around -inf

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

   7. Applied rewrites 38.6%

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

   8. Taylor expanded in y0 around 0

      \[\leadsto y \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 32.1%

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

   11. Taylor expanded in j around 0

       \[\leadsto y \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right) + \left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 30.2%

       \[\leadsto y \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right) + \left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right) \]

   if -1.0592487913441096e-262 < b < 1.6115288797132272e-212

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

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

   if 1.6115288797132272e-212 < b < 1096.8954990076757

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

Alternative 12: 35.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} t_1 := j \cdot x - k \cdot z\\ \mathbf{if}\;y5 \leq -5.993118298644953 \cdot 10^{+197}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -1.1147717578934128 \cdot 10^{-10}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot t\_1\right)\\ \mathbf{elif}\;y5 \leq -1.303784269745559 \cdot 10^{-83}:\\ \;\;\;\;c \cdot \left(\mathsf{fma}\left(-1, i \cdot \left(x \cdot y - t \cdot z\right), x \cdot \left(y0 \cdot y2\right)\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3573781470775196 \cdot 10^{-71}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot t\_1\right)\\ \mathbf{elif}\;y5 \leq 2.606390754857673 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- (* j x) (* k z))))
  (if (<= y5 -5.993118298644953e+197)
    (* y (* y5 (- (* i k) (* a y3))))
    (if (<= y5 -1.1147717578934128e-10)
      (* y0 (- (* c (- (* x y2) (* y3 z))) (* b t_1)))
      (if (<= y5 -1.303784269745559e-83)
        (*
         c
         (-
          (fma -1.0 (* i (- (* x y) (* t z))) (* x (* y0 y2)))
          (* t (* y2 y4))))
        (if (<= y5 1.3573781470775196e-71)
          (- (* b (* y4 (- (* j t) (* k y)))) (* b (* y0 t_1)))
          (if (<= y5 2.606390754857673e+70)
            (+
             (* y (* a (- (* b x) (* y3 y5))))
             (* (- (* k y2) (* j y3)) (* y1 y4)))
            (* a (* y5 (- (* t y2) (* y y3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * x) - (k * z);
	double tmp;
	if (y5 <= -5.993118298644953e+197) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -1.1147717578934128e-10) {
		tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1));
	} else if (y5 <= -1.303784269745559e-83) {
		tmp = c * (fma(-1.0, (i * ((x * y) - (t * z))), (x * (y0 * y2))) - (t * (y2 * y4)));
	} else if (y5 <= 1.3573781470775196e-71) {
		tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1));
	} else if (y5 <= 2.606390754857673e+70) {
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * x) - Float64(k * z))
	tmp = 0.0
	if (y5 <= -5.993118298644953e+197)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y5 <= -1.1147717578934128e-10)
		tmp = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(y3 * z))) - Float64(b * t_1)));
	elseif (y5 <= -1.303784269745559e-83)
		tmp = Float64(c * Float64(fma(-1.0, Float64(i * Float64(Float64(x * y) - Float64(t * z))), Float64(x * Float64(y0 * y2))) - Float64(t * Float64(y2 * y4))));
	elseif (y5 <= 1.3573781470775196e-71)
		tmp = Float64(Float64(b * Float64(y4 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(b * Float64(y0 * t_1)));
	elseif (y5 <= 2.606390754857673e+70)
		tmp = Float64(Float64(y * Float64(a * Float64(Float64(b * x) - Float64(y3 * y5)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(y1 * y4)));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * 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[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -5.993118298644953e+197], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.1147717578934128e-10], N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.303784269745559e-83], N[(c * N[(N[(-1.0 * N[(i * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.3573781470775196e-71], N[(N[(b * N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.606390754857673e+70], N[(N[(y * N[(a * N[(N[(b * x), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = ((j * x) - (k * z)) IN
		LET tmp_4 = IF (y5 <= (26063907548576728971631686428864023329164576046193849429570315689656320)) THEN ((y * (a * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4))) ELSE (a * (y5 * ((t * y2) - (y * y3)))) ENDIF IN
		LET tmp_3 = IF (y5 <= (1357378147077519553045795512739226940749237517690107053345973358988922173254076506071522486650561235026940281266670269357037454476652677794963480386447510409188254054043215276505185418187693358049727976322174072265625e-287)) THEN ((b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1))) ELSE tmp_4 ENDIF IN
		LET tmp_2 = IF (y5 <= (-130378426974555906923998908621579890046376077126584021130028482047185066145859324151673633997127125106237733899893621292420223215430676500957865629088755639838811416550887682727002206745399078894579077136928191293918644078075885772705078125e-322)) THEN (c * ((((-1) * (i * ((x * y) - (t * z)))) + (x * (y0 * y2))) - (t * (y2 * y4)))) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (y5 <= (-111477175789341277561069168031658571660358347799046896398067474365234375e-81)) THEN (y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (y5 <= (-599311829864495254132774625413578543419889134692646568634158903736403693172936764208399141656270852478853926238872109570192497108449162319121145642684480266010900795586683676704034229901829502664704)) THEN (y * (y5 * ((i * k) - (a * y3)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 6 regimes

2. if y5 < -5.9931182986449525e197

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]

   if -5.9931182986449525e197 < y5 < -1.1147717578934128e-10

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in y5 around 0

      \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 34.7%

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

   if -1.1147717578934128e-10 < y5 < -1.3037842697455591e-83

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in c around inf

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

   7. Applied rewrites 34.3%

      \[\leadsto c \cdot \left(\mathsf{fma}\left(-1, i \cdot \left(x \cdot y - t \cdot z\right), x \cdot \left(y0 \cdot y2\right)\right) - t \cdot \left(y2 \cdot y4\right)\right) \]

   if -1.3037842697455591e-83 < y5 < 1.3573781470775196e-71

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in y2 around 0

      \[\leadsto \left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 38.3%

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

   8. Taylor expanded in i around 0

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

   10. Applied rewrites 31.6%

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

   11. Taylor expanded in a around 0

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 32.2%

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   if 1.3573781470775196e-71 < y5 < 2.6063907548576729e70

   1. Initial program 29.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 36.4%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 37.7%

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

   8. Taylor expanded in y0 around 0

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

   10. Applied rewrites 33.6%

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

   if 2.6063907548576729e70 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 13: 35.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} t_1 := j \cdot x - k \cdot z\\ \mathbf{if}\;y5 \leq -5.993118298644953 \cdot 10^{+197}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -1.0362288813268223 \cdot 10^{-26}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot t\_1\right)\\ \mathbf{elif}\;y5 \leq -4.9208428309729876 \cdot 10^{-61}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3573781470775196 \cdot 10^{-71}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot t\_1\right)\\ \mathbf{elif}\;y5 \leq 2.606390754857673 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- (* j x) (* k z))))
  (if (<= y5 -5.993118298644953e+197)
    (* y (* y5 (- (* i k) (* a y3))))
    (if (<= y5 -1.0362288813268223e-26)
      (* y0 (- (* c (- (* x y2) (* y3 z))) (* b t_1)))
      (if (<= y5 -4.9208428309729876e-61)
        (* y4 (* y2 (- (* k y1) (* c t))))
        (if (<= y5 1.3573781470775196e-71)
          (- (* b (* y4 (- (* j t) (* k y)))) (* b (* y0 t_1)))
          (if (<= y5 2.606390754857673e+70)
            (+
             (* y (* a (- (* b x) (* y3 y5))))
             (* (- (* k y2) (* j y3)) (* y1 y4)))
            (* a (* y5 (- (* t y2) (* y y3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * x) - (k * z);
	double tmp;
	if (y5 <= -5.993118298644953e+197) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -1.0362288813268223e-26) {
		tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1));
	} else if (y5 <= -4.9208428309729876e-61) {
		tmp = y4 * (y2 * ((k * y1) - (c * t)));
	} else if (y5 <= 1.3573781470775196e-71) {
		tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1));
	} else if (y5 <= 2.606390754857673e+70) {
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * x) - (k * z)
    if (y5 <= (-5.993118298644953d+197)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y5 <= (-1.0362288813268223d-26)) then
        tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1))
    else if (y5 <= (-4.9208428309729876d-61)) then
        tmp = y4 * (y2 * ((k * y1) - (c * t)))
    else if (y5 <= 1.3573781470775196d-71) then
        tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1))
    else if (y5 <= 2.606390754857673d+70) then
        tmp = (y * (a * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4))
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * x) - (k * z);
	double tmp;
	if (y5 <= -5.993118298644953e+197) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -1.0362288813268223e-26) {
		tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1));
	} else if (y5 <= -4.9208428309729876e-61) {
		tmp = y4 * (y2 * ((k * y1) - (c * t)));
	} else if (y5 <= 1.3573781470775196e-71) {
		tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1));
	} else if (y5 <= 2.606390754857673e+70) {
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (j * x) - (k * z)
	tmp = 0
	if y5 <= -5.993118298644953e+197:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y5 <= -1.0362288813268223e-26:
		tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1))
	elif y5 <= -4.9208428309729876e-61:
		tmp = y4 * (y2 * ((k * y1) - (c * t)))
	elif y5 <= 1.3573781470775196e-71:
		tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1))
	elif y5 <= 2.606390754857673e+70:
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4))
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * x) - Float64(k * z))
	tmp = 0.0
	if (y5 <= -5.993118298644953e+197)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y5 <= -1.0362288813268223e-26)
		tmp = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(y3 * z))) - Float64(b * t_1)));
	elseif (y5 <= -4.9208428309729876e-61)
		tmp = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(c * t))));
	elseif (y5 <= 1.3573781470775196e-71)
		tmp = Float64(Float64(b * Float64(y4 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(b * Float64(y0 * t_1)));
	elseif (y5 <= 2.606390754857673e+70)
		tmp = Float64(Float64(y * Float64(a * Float64(Float64(b * x) - Float64(y3 * y5)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(y1 * y4)));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (j * x) - (k * z);
	tmp = 0.0;
	if (y5 <= -5.993118298644953e+197)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y5 <= -1.0362288813268223e-26)
		tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1));
	elseif (y5 <= -4.9208428309729876e-61)
		tmp = y4 * (y2 * ((k * y1) - (c * t)));
	elseif (y5 <= 1.3573781470775196e-71)
		tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1));
	elseif (y5 <= 2.606390754857673e+70)
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4));
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -5.993118298644953e+197], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.0362288813268223e-26], N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.9208428309729876e-61], N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(c * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.3573781470775196e-71], N[(N[(b * N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.606390754857673e+70], N[(N[(y * N[(a * N[(N[(b * x), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = ((j * x) - (k * z)) IN
		LET tmp_4 = IF (y5 <= (26063907548576728971631686428864023329164576046193849429570315689656320)) THEN ((y * (a * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4))) ELSE (a * (y5 * ((t * y2) - (y * y3)))) ENDIF IN
		LET tmp_3 = IF (y5 <= (1357378147077519553045795512739226940749237517690107053345973358988922173254076506071522486650561235026940281266670269357037454476652677794963480386447510409188254054043215276505185418187693358049727976322174072265625e-287)) THEN ((b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1))) ELSE tmp_4 ENDIF IN
		LET tmp_2 = IF (y5 <= (-492084283097298763714450458858771254176341629763498462549631347263217558353417864107780271055256489565950849640438880144606315842716516929158681147439373393392969546766835264861583709716796875e-252)) THEN (y4 * (y2 * ((k * y1) - (c * t)))) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (y5 <= (-10362288813268222955300149858079322808737133988020938272336303278046108766741184581405832432210445404052734375e-135)) THEN (y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (y5 <= (-599311829864495254132774625413578543419889134692646568634158903736403693172936764208399141656270852478853926238872109570192497108449162319121145642684480266010900795586683676704034229901829502664704)) THEN (y * (y5 * ((i * k) - (a * y3)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 6 regimes

2. if y5 < -5.9931182986449525e197

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]

   if -5.9931182986449525e197 < y5 < -1.0362288813268223e-26

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in y5 around 0

      \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 34.7%

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

   if -1.0362288813268223e-26 < y5 < -4.9208428309729876e-61

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y2 around inf

      \[\leadsto y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

      \[\leadsto y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right) \]

   if -4.9208428309729876e-61 < y5 < 1.3573781470775196e-71

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in y2 around 0

      \[\leadsto \left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 38.3%

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

   8. Taylor expanded in i around 0

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

   10. Applied rewrites 31.6%

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

   11. Taylor expanded in a around 0

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 32.2%

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   if 1.3573781470775196e-71 < y5 < 2.6063907548576729e70

   1. Initial program 29.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 36.4%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 37.7%

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

   8. Taylor expanded in y0 around 0

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

   10. Applied rewrites 33.6%

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

   if 2.6063907548576729e70 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 14: 35.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} t_1 := j \cdot x - k \cdot z\\ \mathbf{if}\;y5 \leq -5.993118298644953 \cdot 10^{+197}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -1.0362288813268223 \cdot 10^{-26}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot t\_1\right)\\ \mathbf{elif}\;y5 \leq -4.9208428309729876 \cdot 10^{-61}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3573781470775196 \cdot 10^{-71}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot t\_1\right)\\ \mathbf{elif}\;y5 \leq 2.606390754857673 \cdot 10^{+70}:\\ \;\;\;\;a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- (* j x) (* k z))))
  (if (<= y5 -5.993118298644953e+197)
    (* y (* y5 (- (* i k) (* a y3))))
    (if (<= y5 -1.0362288813268223e-26)
      (* y0 (- (* c (- (* x y2) (* y3 z))) (* b t_1)))
      (if (<= y5 -4.9208428309729876e-61)
        (* y4 (* y2 (- (* k y1) (* c t))))
        (if (<= y5 1.3573781470775196e-71)
          (- (* b (* y4 (- (* j t) (* k y)))) (* b (* y0 t_1)))
          (if (<= y5 2.606390754857673e+70)
            (+
             (* a (* y (- (* b x) (* y3 y5))))
             (* (- (* k y2) (* j y3)) (* y1 y4)))
            (* a (* y5 (- (* t y2) (* y y3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * x) - (k * z);
	double tmp;
	if (y5 <= -5.993118298644953e+197) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -1.0362288813268223e-26) {
		tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1));
	} else if (y5 <= -4.9208428309729876e-61) {
		tmp = y4 * (y2 * ((k * y1) - (c * t)));
	} else if (y5 <= 1.3573781470775196e-71) {
		tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1));
	} else if (y5 <= 2.606390754857673e+70) {
		tmp = (a * (y * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * x) - (k * z)
    if (y5 <= (-5.993118298644953d+197)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y5 <= (-1.0362288813268223d-26)) then
        tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1))
    else if (y5 <= (-4.9208428309729876d-61)) then
        tmp = y4 * (y2 * ((k * y1) - (c * t)))
    else if (y5 <= 1.3573781470775196d-71) then
        tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1))
    else if (y5 <= 2.606390754857673d+70) then
        tmp = (a * (y * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4))
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * x) - (k * z);
	double tmp;
	if (y5 <= -5.993118298644953e+197) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -1.0362288813268223e-26) {
		tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1));
	} else if (y5 <= -4.9208428309729876e-61) {
		tmp = y4 * (y2 * ((k * y1) - (c * t)));
	} else if (y5 <= 1.3573781470775196e-71) {
		tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1));
	} else if (y5 <= 2.606390754857673e+70) {
		tmp = (a * (y * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (j * x) - (k * z)
	tmp = 0
	if y5 <= -5.993118298644953e+197:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y5 <= -1.0362288813268223e-26:
		tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1))
	elif y5 <= -4.9208428309729876e-61:
		tmp = y4 * (y2 * ((k * y1) - (c * t)))
	elif y5 <= 1.3573781470775196e-71:
		tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1))
	elif y5 <= 2.606390754857673e+70:
		tmp = (a * (y * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4))
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * x) - Float64(k * z))
	tmp = 0.0
	if (y5 <= -5.993118298644953e+197)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y5 <= -1.0362288813268223e-26)
		tmp = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(y3 * z))) - Float64(b * t_1)));
	elseif (y5 <= -4.9208428309729876e-61)
		tmp = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(c * t))));
	elseif (y5 <= 1.3573781470775196e-71)
		tmp = Float64(Float64(b * Float64(y4 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(b * Float64(y0 * t_1)));
	elseif (y5 <= 2.606390754857673e+70)
		tmp = Float64(Float64(a * Float64(y * Float64(Float64(b * x) - Float64(y3 * y5)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(y1 * y4)));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (j * x) - (k * z);
	tmp = 0.0;
	if (y5 <= -5.993118298644953e+197)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y5 <= -1.0362288813268223e-26)
		tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1));
	elseif (y5 <= -4.9208428309729876e-61)
		tmp = y4 * (y2 * ((k * y1) - (c * t)));
	elseif (y5 <= 1.3573781470775196e-71)
		tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1));
	elseif (y5 <= 2.606390754857673e+70)
		tmp = (a * (y * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4));
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -5.993118298644953e+197], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.0362288813268223e-26], N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.9208428309729876e-61], N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(c * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.3573781470775196e-71], N[(N[(b * N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.606390754857673e+70], N[(N[(a * N[(y * N[(N[(b * x), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = ((j * x) - (k * z)) IN
		LET tmp_4 = IF (y5 <= (26063907548576728971631686428864023329164576046193849429570315689656320)) THEN ((a * (y * ((b * x) - (y3 * y5)))) + (((k * y2) - (j * y3)) * (y1 * y4))) ELSE (a * (y5 * ((t * y2) - (y * y3)))) ENDIF IN
		LET tmp_3 = IF (y5 <= (1357378147077519553045795512739226940749237517690107053345973358988922173254076506071522486650561235026940281266670269357037454476652677794963480386447510409188254054043215276505185418187693358049727976322174072265625e-287)) THEN ((b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1))) ELSE tmp_4 ENDIF IN
		LET tmp_2 = IF (y5 <= (-492084283097298763714450458858771254176341629763498462549631347263217558353417864107780271055256489565950849640438880144606315842716516929158681147439373393392969546766835264861583709716796875e-252)) THEN (y4 * (y2 * ((k * y1) - (c * t)))) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (y5 <= (-10362288813268222955300149858079322808737133988020938272336303278046108766741184581405832432210445404052734375e-135)) THEN (y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (y5 <= (-599311829864495254132774625413578543419889134692646568634158903736403693172936764208399141656270852478853926238872109570192497108449162319121145642684480266010900795586683676704034229901829502664704)) THEN (y * (y5 * ((i * k) - (a * y3)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 6 regimes

2. if y5 < -5.9931182986449525e197

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]

   if -5.9931182986449525e197 < y5 < -1.0362288813268223e-26

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in y5 around 0

      \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 34.7%

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

   if -1.0362288813268223e-26 < y5 < -4.9208428309729876e-61

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y2 around inf

      \[\leadsto y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

      \[\leadsto y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right) \]

   if -4.9208428309729876e-61 < y5 < 1.3573781470775196e-71

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in y2 around 0

      \[\leadsto \left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 38.3%

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

   8. Taylor expanded in i around 0

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

   10. Applied rewrites 31.6%

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

   11. Taylor expanded in a around 0

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 32.2%

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   if 1.3573781470775196e-71 < y5 < 2.6063907548576729e70

   1. Initial program 29.3%

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

   2. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.3%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 38.0%

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

   8. Taylor expanded in y0 around 0

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

   10. Applied rewrites 33.7%

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

   if 2.6063907548576729e70 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 15: 35.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} t_1 := j \cdot x - k \cdot z\\ \mathbf{if}\;y5 \leq -5.993118298644953 \cdot 10^{+197}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -1.0362288813268223 \cdot 10^{-26}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot t\_1\right)\\ \mathbf{elif}\;y5 \leq -4.9208428309729876 \cdot 10^{-61}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 1.5592210734074937 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot t\_1\right)\\ \mathbf{elif}\;y5 \leq 3.635865257040308 \cdot 10^{+219}:\\ \;\;\;\;-1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- (* j x) (* k z))))
  (if (<= y5 -5.993118298644953e+197)
    (* y (* y5 (- (* i k) (* a y3))))
    (if (<= y5 -1.0362288813268223e-26)
      (* y0 (- (* c (- (* x y2) (* y3 z))) (* b t_1)))
      (if (<= y5 -4.9208428309729876e-61)
        (* y4 (* y2 (- (* k y1) (* c t))))
        (if (<= y5 1.5592210734074937e+60)
          (- (* b (* y4 (- (* j t) (* k y)))) (* b (* y0 t_1)))
          (if (<= y5 3.635865257040308e+219)
            (* -1.0 (* a (* t (- (* b z) (* y2 y5)))))
            (* a (* y5 (- (* t y2) (* y y3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * x) - (k * z);
	double tmp;
	if (y5 <= -5.993118298644953e+197) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -1.0362288813268223e-26) {
		tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1));
	} else if (y5 <= -4.9208428309729876e-61) {
		tmp = y4 * (y2 * ((k * y1) - (c * t)));
	} else if (y5 <= 1.5592210734074937e+60) {
		tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1));
	} else if (y5 <= 3.635865257040308e+219) {
		tmp = -1.0 * (a * (t * ((b * z) - (y2 * y5))));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * x) - (k * z)
    if (y5 <= (-5.993118298644953d+197)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y5 <= (-1.0362288813268223d-26)) then
        tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1))
    else if (y5 <= (-4.9208428309729876d-61)) then
        tmp = y4 * (y2 * ((k * y1) - (c * t)))
    else if (y5 <= 1.5592210734074937d+60) then
        tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1))
    else if (y5 <= 3.635865257040308d+219) then
        tmp = (-1.0d0) * (a * (t * ((b * z) - (y2 * y5))))
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * x) - (k * z);
	double tmp;
	if (y5 <= -5.993118298644953e+197) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -1.0362288813268223e-26) {
		tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1));
	} else if (y5 <= -4.9208428309729876e-61) {
		tmp = y4 * (y2 * ((k * y1) - (c * t)));
	} else if (y5 <= 1.5592210734074937e+60) {
		tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1));
	} else if (y5 <= 3.635865257040308e+219) {
		tmp = -1.0 * (a * (t * ((b * z) - (y2 * y5))));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (j * x) - (k * z)
	tmp = 0
	if y5 <= -5.993118298644953e+197:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y5 <= -1.0362288813268223e-26:
		tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1))
	elif y5 <= -4.9208428309729876e-61:
		tmp = y4 * (y2 * ((k * y1) - (c * t)))
	elif y5 <= 1.5592210734074937e+60:
		tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1))
	elif y5 <= 3.635865257040308e+219:
		tmp = -1.0 * (a * (t * ((b * z) - (y2 * y5))))
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * x) - Float64(k * z))
	tmp = 0.0
	if (y5 <= -5.993118298644953e+197)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y5 <= -1.0362288813268223e-26)
		tmp = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(y3 * z))) - Float64(b * t_1)));
	elseif (y5 <= -4.9208428309729876e-61)
		tmp = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(c * t))));
	elseif (y5 <= 1.5592210734074937e+60)
		tmp = Float64(Float64(b * Float64(y4 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(b * Float64(y0 * t_1)));
	elseif (y5 <= 3.635865257040308e+219)
		tmp = Float64(-1.0 * Float64(a * Float64(t * Float64(Float64(b * z) - Float64(y2 * y5)))));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (j * x) - (k * z);
	tmp = 0.0;
	if (y5 <= -5.993118298644953e+197)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y5 <= -1.0362288813268223e-26)
		tmp = y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1));
	elseif (y5 <= -4.9208428309729876e-61)
		tmp = y4 * (y2 * ((k * y1) - (c * t)));
	elseif (y5 <= 1.5592210734074937e+60)
		tmp = (b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1));
	elseif (y5 <= 3.635865257040308e+219)
		tmp = -1.0 * (a * (t * ((b * z) - (y2 * y5))));
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -5.993118298644953e+197], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.0362288813268223e-26], N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.9208428309729876e-61], N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(c * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.5592210734074937e+60], N[(N[(b * N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.635865257040308e+219], N[(-1.0 * N[(a * N[(t * N[(N[(b * z), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = ((j * x) - (k * z)) IN
		LET tmp_4 = IF (y5 <= (3635865257040308124040583854993653764981413933252370898635781988785109879589342532700529748506353778313658859036754300012601121471209276657687754958074107019884362536536064049840668964733168923854042614806727875236986880)) THEN ((-1) * (a * (t * ((b * z) - (y2 * y5))))) ELSE (a * (y5 * ((t * y2) - (y * y3)))) ENDIF IN
		LET tmp_3 = IF (y5 <= (1559221073407493671536076383776403975298610075874980674928640)) THEN ((b * (y4 * ((j * t) - (k * y)))) - (b * (y0 * t_1))) ELSE tmp_4 ENDIF IN
		LET tmp_2 = IF (y5 <= (-492084283097298763714450458858771254176341629763498462549631347263217558353417864107780271055256489565950849640438880144606315842716516929158681147439373393392969546766835264861583709716796875e-252)) THEN (y4 * (y2 * ((k * y1) - (c * t)))) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (y5 <= (-10362288813268222955300149858079322808737133988020938272336303278046108766741184581405832432210445404052734375e-135)) THEN (y0 * ((c * ((x * y2) - (y3 * z))) - (b * t_1))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (y5 <= (-599311829864495254132774625413578543419889134692646568634158903736403693172936764208399141656270852478853926238872109570192497108449162319121145642684480266010900795586683676704034229901829502664704)) THEN (y * (y5 * ((i * k) - (a * y3)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 6 regimes

2. if y5 < -5.9931182986449525e197

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]

   if -5.9931182986449525e197 < y5 < -1.0362288813268223e-26

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in y5 around 0

      \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 34.7%

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

   if -1.0362288813268223e-26 < y5 < -4.9208428309729876e-61

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y2 around inf

      \[\leadsto y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

      \[\leadsto y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right) \]

   if -4.9208428309729876e-61 < y5 < 1.5592210734074937e60

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in y2 around 0

      \[\leadsto \left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 38.3%

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

   8. Taylor expanded in i around 0

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

   10. Applied rewrites 31.6%

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

   11. Taylor expanded in a around 0

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 32.2%

       \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - b \cdot \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   if 1.5592210734074937e60 < y5 < 3.6358652570403081e219

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(x \cdot \left(y1 \cdot y2\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto a \cdot \left(\mathsf{fma}\left(-1, x \cdot \left(y1 \cdot y2\right), b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]

   8. Taylor expanded in t around -inf

      \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 25.7%

       \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right) \]

   if 3.6358652570403081e219 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 16: 35.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} t_1 := y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0\right)\right)\\ \mathbf{if}\;j \leq -1.4563404196238097 \cdot 10^{+262}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -4.902233246643102 \cdot 10^{+150}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(-1 \cdot \left(y3 \cdot z\right)\right) - b \cdot \left(j \cdot x\right)\right)\\ \mathbf{elif}\;j \leq -3.098684433340073 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -9.689096634541713 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.3924521065548745 \cdot 10^{-87}:\\ \;\;\;\;y \cdot \left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right) + \left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{elif}\;j \leq 1.1570482074290145 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* y2 (fma k (- (* y1 y4) (* y0 y5)) (* x (* c y0))))))
  (if (<= j -1.4563404196238097e+262)
    (* b (* j (- (* t y4) (* x y0))))
    (if (<= j -4.902233246643102e+150)
      (* y0 (- (* c (* -1.0 (* y3 z))) (* b (* j x))))
      (if (<= j -3.098684433340073e-71)
        (* t (* y4 (- (* b j) (* c y2))))
        (if (<= j -9.689096634541713e-171)
          t_1
          (if (<= j 2.3924521065548745e-87)
            (+
             (* y (* a (- (* b x) (* y3 y5))))
             (* (* k y2) (* y1 y4)))
            (if (<= j 1.1570482074290145e+100)
              t_1
              (* -1.0 (* y3 (* y4 (- (* j y1) (* c 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 t_1 = y2 * fma(k, ((y1 * y4) - (y0 * y5)), (x * (c * y0)));
	double tmp;
	if (j <= -1.4563404196238097e+262) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (j <= -4.902233246643102e+150) {
		tmp = y0 * ((c * (-1.0 * (y3 * z))) - (b * (j * x)));
	} else if (j <= -3.098684433340073e-71) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (j <= -9.689096634541713e-171) {
		tmp = t_1;
	} else if (j <= 2.3924521065548745e-87) {
		tmp = (y * (a * ((b * x) - (y3 * y5)))) + ((k * y2) * (y1 * y4));
	} else if (j <= 1.1570482074290145e+100) {
		tmp = t_1;
	} else {
		tmp = -1.0 * (y3 * (y4 * ((j * y1) - (c * y))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(x * Float64(c * y0))))
	tmp = 0.0
	if (j <= -1.4563404196238097e+262)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (j <= -4.902233246643102e+150)
		tmp = Float64(y0 * Float64(Float64(c * Float64(-1.0 * Float64(y3 * z))) - Float64(b * Float64(j * x))));
	elseif (j <= -3.098684433340073e-71)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (j <= -9.689096634541713e-171)
		tmp = t_1;
	elseif (j <= 2.3924521065548745e-87)
		tmp = Float64(Float64(y * Float64(a * Float64(Float64(b * x) - Float64(y3 * y5)))) + Float64(Float64(k * y2) * Float64(y1 * y4)));
	elseif (j <= 1.1570482074290145e+100)
		tmp = t_1;
	else
		tmp = Float64(-1.0 * Float64(y3 * Float64(y4 * Float64(Float64(j * y1) - Float64(c * y)))));
	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[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(x * N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.4563404196238097e+262], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.902233246643102e+150], N[(y0 * N[(N[(c * N[(-1.0 * N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.098684433340073e-71], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -9.689096634541713e-171], t$95$1, If[LessEqual[j, 2.3924521065548745e-87], N[(N[(y * N[(a * N[(N[(b * x), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * y2), $MachinePrecision] * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.1570482074290145e+100], t$95$1, N[(-1.0 * N[(y3 * N[(y4 * N[(N[(j * y1), $MachinePrecision] - N[(c * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (y2 * ((k * ((y1 * y4) - (y0 * y5))) + (x * (c * y0)))) IN
		LET tmp_5 = IF (j <= (11570482074290145409857180326035211155432798210328288062774200607193234350636361207785554307503357952)) THEN t_1 ELSE ((-1) * (y3 * (y4 * ((j * y1) - (c * y))))) ENDIF IN
		LET tmp_4 = IF (j <= (239245210655487452056155815089472168436244312943299019449801469014643461988493053369783303319176316522907007805299185768477680977171072380346905251110104307752194724206572794848574012236883776897390947530224500176820878749595067347399890422821044921875e-338)) THEN ((y * (a * ((b * x) - (y3 * y5)))) + ((k * y2) * (y1 * y4))) ELSE tmp_5 ENDIF IN
		LET tmp_3 = IF (j <= (-968909663454171315204996975159806292403516262244265750323474896782458879457793385996603508952393039808181917168488902476765377217603462538370722492905824005605915818057342783317818958323744097743452410757470839861578350398064516888787004775658914015718343974037004019461597765261792048680762391406897123111909508363073330632032956172141479690648425684834402581684836147520112648696312114433524592011184764332731855773772622342221438884735107421875e-617)) THEN t_1 ELSE tmp_4 ENDIF IN
		LET tmp_2 = IF (j <= (-309868443334007283537103453418361256062039805292327374992828678630938810831425384589765796650278698276873349195420073776306904677976452748746245369171164171454322898252882055765422553150756357354111969470977783203125e-286)) THEN (t * (y4 * ((b * j) - (c * y2)))) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (j <= (-4902233246643102314553892138126026727926934824490854365474924894129433304936400590985007399634151280395415844709788459770401806571107752914495798771712)) THEN (y0 * ((c * ((-1) * (y3 * z))) - (b * (j * x)))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (j <= (-14563404196238097104449860189983365686264013320765645412392823603311374113176708449825308047181060795949270125238310000685302088863227147339640020048109863847819272800610710057363886169409952925116656282553885797952180901913965403322134082513398556295696733962240)) THEN (b * (j * ((t * y4) - (x * y0)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 6 regimes

2. if j < -1.4563404196238097e262

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

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

   if -1.4563404196238097e262 < j < -4.9022332466431023e150

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in y5 around 0

      \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 34.7%

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

   8. Taylor expanded in x around inf

      \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 31.6%

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

   11. Taylor expanded in x around 0

       \[\leadsto y0 \cdot \left(c \cdot \left(-1 \cdot \left(y3 \cdot z\right)\right) - b \cdot \left(j \cdot x\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 27.1%

       \[\leadsto y0 \cdot \left(c \cdot \left(-1 \cdot \left(y3 \cdot z\right)\right) - b \cdot \left(j \cdot x\right)\right) \]

   if -4.9022332466431023e150 < j < -3.0986844333400728e-71

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]

   if -3.0986844333400728e-71 < j < -9.6890966345417132e-171 or 2.3924521065548745e-87 < j < 1.1570482074290145e100

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

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

   8. Taylor expanded in a around 0

      \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 32.1%

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

   if -9.6890966345417132e-171 < j < 2.3924521065548745e-87

   1. Initial program 29.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 36.4%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 37.7%

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

   8. Taylor expanded in y0 around 0

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

   10. Applied rewrites 33.6%

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

   11. Taylor expanded in j around 0

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

   13. Applied rewrites 31.8%

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

   if 1.1570482074290145e100 < j

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y4 around inf

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

   7. Applied rewrites 26.6%

      \[\leadsto -1 \cdot \left(y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 17: 33.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} t_1 := y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0\right)\right)\\ \mathbf{if}\;j \leq -1.4563404196238097 \cdot 10^{+262}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -4.902233246643102 \cdot 10^{+150}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(-1 \cdot \left(y3 \cdot z\right)\right) - b \cdot \left(j \cdot x\right)\right)\\ \mathbf{elif}\;j \leq -3.098684433340073 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -1.1281776376114543 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.3924521065548745 \cdot 10^{-87}:\\ \;\;\;\;a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right) + \left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{elif}\;j \leq 1.1570482074290145 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* y2 (fma k (- (* y1 y4) (* y0 y5)) (* x (* c y0))))))
  (if (<= j -1.4563404196238097e+262)
    (* b (* j (- (* t y4) (* x y0))))
    (if (<= j -4.902233246643102e+150)
      (* y0 (- (* c (* -1.0 (* y3 z))) (* b (* j x))))
      (if (<= j -3.098684433340073e-71)
        (* t (* y4 (- (* b j) (* c y2))))
        (if (<= j -1.1281776376114543e-170)
          t_1
          (if (<= j 2.3924521065548745e-87)
            (+
             (* a (* y (- (* b x) (* y3 y5))))
             (* (* k y2) (* y1 y4)))
            (if (<= j 1.1570482074290145e+100)
              t_1
              (* -1.0 (* y3 (* y4 (- (* j y1) (* c 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 t_1 = y2 * fma(k, ((y1 * y4) - (y0 * y5)), (x * (c * y0)));
	double tmp;
	if (j <= -1.4563404196238097e+262) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (j <= -4.902233246643102e+150) {
		tmp = y0 * ((c * (-1.0 * (y3 * z))) - (b * (j * x)));
	} else if (j <= -3.098684433340073e-71) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (j <= -1.1281776376114543e-170) {
		tmp = t_1;
	} else if (j <= 2.3924521065548745e-87) {
		tmp = (a * (y * ((b * x) - (y3 * y5)))) + ((k * y2) * (y1 * y4));
	} else if (j <= 1.1570482074290145e+100) {
		tmp = t_1;
	} else {
		tmp = -1.0 * (y3 * (y4 * ((j * y1) - (c * y))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(x * Float64(c * y0))))
	tmp = 0.0
	if (j <= -1.4563404196238097e+262)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (j <= -4.902233246643102e+150)
		tmp = Float64(y0 * Float64(Float64(c * Float64(-1.0 * Float64(y3 * z))) - Float64(b * Float64(j * x))));
	elseif (j <= -3.098684433340073e-71)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (j <= -1.1281776376114543e-170)
		tmp = t_1;
	elseif (j <= 2.3924521065548745e-87)
		tmp = Float64(Float64(a * Float64(y * Float64(Float64(b * x) - Float64(y3 * y5)))) + Float64(Float64(k * y2) * Float64(y1 * y4)));
	elseif (j <= 1.1570482074290145e+100)
		tmp = t_1;
	else
		tmp = Float64(-1.0 * Float64(y3 * Float64(y4 * Float64(Float64(j * y1) - Float64(c * y)))));
	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[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(x * N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.4563404196238097e+262], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.902233246643102e+150], N[(y0 * N[(N[(c * N[(-1.0 * N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.098684433340073e-71], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.1281776376114543e-170], t$95$1, If[LessEqual[j, 2.3924521065548745e-87], N[(N[(a * N[(y * N[(N[(b * x), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * y2), $MachinePrecision] * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.1570482074290145e+100], t$95$1, N[(-1.0 * N[(y3 * N[(y4 * N[(N[(j * y1), $MachinePrecision] - N[(c * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (y2 * ((k * ((y1 * y4) - (y0 * y5))) + (x * (c * y0)))) IN
		LET tmp_5 = IF (j <= (11570482074290145409857180326035211155432798210328288062774200607193234350636361207785554307503357952)) THEN t_1 ELSE ((-1) * (y3 * (y4 * ((j * y1) - (c * y))))) ENDIF IN
		LET tmp_4 = IF (j <= (239245210655487452056155815089472168436244312943299019449801469014643461988493053369783303319176316522907007805299185768477680977171072380346905251110104307752194724206572794848574012236883776897390947530224500176820878749595067347399890422821044921875e-338)) THEN ((a * (y * ((b * x) - (y3 * y5)))) + ((k * y2) * (y1 * y4))) ELSE tmp_5 ENDIF IN
		LET tmp_3 = IF (j <= (-1128177637611454251615404807184721951283052303608896513007149894054730052578112102239563099881013191502402724241988807397136098629037033424865284600562583039918176072202654971030593989475431644046565835385191666555468149574522837797342078582772820109506206210744471934691943791488395573569695933113100394326969515798386481355836402058550754900492619747870364405615868041155030180150244430474016931639273338995599349487974905059672892093658447265625e-617)) THEN t_1 ELSE tmp_4 ENDIF IN
		LET tmp_2 = IF (j <= (-309868443334007283537103453418361256062039805292327374992828678630938810831425384589765796650278698276873349195420073776306904677976452748746245369171164171454322898252882055765422553150756357354111969470977783203125e-286)) THEN (t * (y4 * ((b * j) - (c * y2)))) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (j <= (-4902233246643102314553892138126026727926934824490854365474924894129433304936400590985007399634151280395415844709788459770401806571107752914495798771712)) THEN (y0 * ((c * ((-1) * (y3 * z))) - (b * (j * x)))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (j <= (-14563404196238097104449860189983365686264013320765645412392823603311374113176708449825308047181060795949270125238310000685302088863227147339640020048109863847819272800610710057363886169409952925116656282553885797952180901913965403322134082513398556295696733962240)) THEN (b * (j * ((t * y4) - (x * y0)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 6 regimes

2. if j < -1.4563404196238097e262

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

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

   if -1.4563404196238097e262 < j < -4.9022332466431023e150

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in y5 around 0

      \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 34.7%

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

   8. Taylor expanded in x around inf

      \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 31.6%

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

   11. Taylor expanded in x around 0

       \[\leadsto y0 \cdot \left(c \cdot \left(-1 \cdot \left(y3 \cdot z\right)\right) - b \cdot \left(j \cdot x\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 27.1%

       \[\leadsto y0 \cdot \left(c \cdot \left(-1 \cdot \left(y3 \cdot z\right)\right) - b \cdot \left(j \cdot x\right)\right) \]

   if -4.9022332466431023e150 < j < -3.0986844333400728e-71

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]

   if -3.0986844333400728e-71 < j < -1.1281776376114543e-170 or 2.3924521065548745e-87 < j < 1.1570482074290145e100

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

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

   8. Taylor expanded in a around 0

      \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 32.1%

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

   if -1.1281776376114543e-170 < j < 2.3924521065548745e-87

   1. Initial program 29.3%

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

   2. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.3%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 38.0%

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

   8. Taylor expanded in y0 around 0

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

   10. Applied rewrites 33.7%

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

   11. Taylor expanded in j around 0

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

   13. Applied rewrites 31.8%

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

   if 1.1570482074290145e100 < j

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y4 around inf

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

   7. Applied rewrites 26.6%

      \[\leadsto -1 \cdot \left(y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 18: 33.7% accurate, 3.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y5 \leq -6.39713093458932 \cdot 10^{+211}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -2.326975990089686 \cdot 10^{-17}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \mathsf{fma}\left(-1, c \cdot z, j \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 1.560182504075062 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 4.642544926929246 \cdot 10^{-110}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)\\ \mathbf{elif}\;y5 \leq 4.311135613447043 \cdot 10^{-6}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(y \cdot \left(b \cdot k - c \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3.023120593344306 \cdot 10^{+223}:\\ \;\;\;\;-1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= y5 -6.39713093458932e+211)
  (* y (* y5 (- (* i k) (* a y3))))
  (if (<= y5 -2.326975990089686e-17)
    (* y0 (* y3 (fma -1.0 (* c z) (* j y5))))
    (if (<= y5 1.560182504075062e-241)
      (* t (* y4 (- (* b j) (* c y2))))
      (if (<= y5 4.642544926929246e-110)
        (* b (* y0 (- (* k z) (* j x))))
        (if (<= y5 4.311135613447043e-6)
          (* y4 (* -1.0 (* y (- (* b k) (* c y3)))))
          (if (<= y5 3.023120593344306e+223)
            (* -1.0 (* a (* t (- (* b z) (* y2 y5)))))
            (* a (* y5 (- (* t y2) (* y y3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -6.39713093458932e+211) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -2.326975990089686e-17) {
		tmp = y0 * (y3 * fma(-1.0, (c * z), (j * y5)));
	} else if (y5 <= 1.560182504075062e-241) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y5 <= 4.642544926929246e-110) {
		tmp = b * (y0 * ((k * z) - (j * x)));
	} else if (y5 <= 4.311135613447043e-6) {
		tmp = y4 * (-1.0 * (y * ((b * k) - (c * y3))));
	} else if (y5 <= 3.023120593344306e+223) {
		tmp = -1.0 * (a * (t * ((b * z) - (y2 * y5))));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -6.39713093458932e+211)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y5 <= -2.326975990089686e-17)
		tmp = Float64(y0 * Float64(y3 * fma(-1.0, Float64(c * z), Float64(j * y5))));
	elseif (y5 <= 1.560182504075062e-241)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y5 <= 4.642544926929246e-110)
		tmp = Float64(b * Float64(y0 * Float64(Float64(k * z) - Float64(j * x))));
	elseif (y5 <= 4.311135613447043e-6)
		tmp = Float64(y4 * Float64(-1.0 * Float64(y * Float64(Float64(b * k) - Float64(c * y3)))));
	elseif (y5 <= 3.023120593344306e+223)
		tmp = Float64(-1.0 * Float64(a * Float64(t * Float64(Float64(b * z) - Float64(y2 * y5)))));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * 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[y5, -6.39713093458932e+211], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.326975990089686e-17], N[(y0 * N[(y3 * N[(-1.0 * N[(c * z), $MachinePrecision] + N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.560182504075062e-241], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.642544926929246e-110], N[(b * N[(y0 * N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.311135613447043e-6], N[(y4 * N[(-1.0 * N[(y * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.023120593344306e+223], N[(-1.0 * N[(a * N[(t * N[(N[(b * z), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_5 = IF (y5 <= (30231205933443062454408435334641792038815400613609636101055778027672173772276083226596013467612608386047804488283231902663920006600073634063448433860304929402104677603980839925373626914486661861692960908045915838003458080768)) THEN ((-1) * (a * (t * ((b * z) - (y2 * y5))))) ELSE (a * (y5 * ((t * y2) - (y * y3)))) ENDIF IN
	LET tmp_4 = IF (y5 <= (431113561344704325473640993404700338942348025739192962646484375e-68)) THEN (y4 * ((-1) * (y * ((b * k) - (c * y3))))) ELSE tmp_5 ENDIF IN
	LET tmp_3 = IF (y5 <= (4642544926929246288565147771407543729019716109620121824726143735864490328778787173993386926836293905706693277692712743089010970186178603993962476741280833763390769630149860813272610529761755858499808545881344137127150075835724364990618450410294450491048521448579351582341967485945133375935256481170654296875e-416)) THEN (b * (y0 * ((k * z) - (j * x)))) ELSE tmp_4 ENDIF IN
	LET tmp_2 = IF (y5 <= (15601825040750618987721862768280761312884375721208656628012215226585772945667304443534717592247664444940740504029442505816557127673993481381001692043669243974835723175581508016962565181893286374579822840298505588925674003172849104711663735773991141591698399120394539730152626584704229847347474526958595950236766833282087052557553321496233064756939982795655629053316546654719144367371032653896703788893641712979894458231038797987966046083476279517927251078602839646793202723573629347142629440195974058062083943561756308696460154971266303726807068201642535366581557681174043106242521616877638734877109527587890625e-851)) THEN (t * (y4 * ((b * j) - (c * y2)))) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (y5 <= (-2326975990089685921723724670422846188013634295514708849594853745657019317150115966796875e-104)) THEN (y0 * (y3 * (((-1) * (c * z)) + (j * y5)))) ELSE tmp_2 ENDIF IN
	LET tmp = IF (y5 <= (-63971309345893201765211847965470960235453125714401346880702311221396693604927144875474724512364862783846773622903709402332571236285077579471935168531929015680333410988621817181367073562910513696115017385596944384)) THEN (y * (y5 * ((i * k) - (a * y3)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 7 regimes

2. if y5 < -6.3971309345893202e211

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]

   if -6.3971309345893202e211 < y5 < -2.3269759900896859e-17

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

   if -2.3269759900896859e-17 < y5 < 1.5601825040750619e-241

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]

   if 1.5601825040750619e-241 < y5 < 4.6425449269292463e-110

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

      \[\leadsto b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right) \]

   if 4.6425449269292463e-110 < y5 < 4.3111356134470433e-6

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

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

   7. Applied rewrites 25.9%

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

   if 4.3111356134470433e-6 < y5 < 3.0231205933443062e223

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(x \cdot \left(y1 \cdot y2\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto a \cdot \left(\mathsf{fma}\left(-1, x \cdot \left(y1 \cdot y2\right), b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]

   8. Taylor expanded in t around -inf

      \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 25.7%

       \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right) \]

   if 3.0231205933443062e223 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
3. Recombined 7 regimes into one program.
4. Add Preprocessing

Alternative 19: 33.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;b \leq -5.167185929603508 \cdot 10^{+235}:\\ \;\;\;\;-1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)\\ \mathbf{elif}\;b \leq -1.3375700603832583 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.6115288797132272 \cdot 10^{-212}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 2.233454878945046 \cdot 10^{+118}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \mathsf{fma}\left(-1, c \cdot z, j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* j (* b (- (* t y4) (* x y0))))))
  (if (<= b -5.167185929603508e+235)
    (* -1.0 (* a (* t (- (* b z) (* y2 y5)))))
    (if (<= b -1.3375700603832583e+50)
      t_1
      (if (<= b 1.6115288797132272e-212)
        (*
         y2
         (fma k (- (* y1 y4) (* y0 y5)) (* x (- (* c y0) (* a y1)))))
        (if (<= b 2.233454878945046e+118)
          (* y0 (* y3 (fma -1.0 (* c z) (* j y5))))
          t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -5.167185929603508e+235) {
		tmp = -1.0 * (a * (t * ((b * z) - (y2 * y5))));
	} else if (b <= -1.3375700603832583e+50) {
		tmp = t_1;
	} else if (b <= 1.6115288797132272e-212) {
		tmp = y2 * fma(k, ((y1 * y4) - (y0 * y5)), (x * ((c * y0) - (a * y1))));
	} else if (b <= 2.233454878945046e+118) {
		tmp = y0 * (y3 * fma(-1.0, (c * z), (j * y5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (b <= -5.167185929603508e+235)
		tmp = Float64(-1.0 * Float64(a * Float64(t * Float64(Float64(b * z) - Float64(y2 * y5)))));
	elseif (b <= -1.3375700603832583e+50)
		tmp = t_1;
	elseif (b <= 1.6115288797132272e-212)
		tmp = Float64(y2 * fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))));
	elseif (b <= 2.233454878945046e+118)
		tmp = Float64(y0 * Float64(y3 * fma(-1.0, Float64(c * z), Float64(j * y5))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.167185929603508e+235], N[(-1.0 * N[(a * N[(t * N[(N[(b * z), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.3375700603832583e+50], t$95$1, If[LessEqual[b, 1.6115288797132272e-212], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.233454878945046e+118], N[(y0 * N[(y3 * N[(-1.0 * N[(c * z), $MachinePrecision] + N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (j * (b * ((t * y4) - (x * y0)))) IN
		LET tmp_3 = IF (b <= (22334548789450461643509347306614627765585692681114701528267652296617185768127828575377205654093831683498965211350564864)) THEN (y0 * (y3 * (((-1) * (c * z)) + (j * y5)))) ELSE t_1 ENDIF IN
		LET tmp_2 = IF (b <= (1611528879713227174050611709674011657656107538605551913366296714592994601470065121364137184602953694863995276970269110631416915841532217873341354389215515582181351185707982512119417956580383981715201739216823125535028354083411396474067673207422685361717573717366712831401789262078057685613036272275617296696302496958406623811574964922193511244093281539082871147418479545677340833854354846475725668388209145095461379372844828710472112611959391701335593724804986569561707661223982821711131508168236649617376110565913904792978428304195404052734375e-755)) THEN (y2 * ((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1))))) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (b <= (-133757006038325832097107320177579983643773956521984)) THEN t_1 ELSE tmp_2 ENDIF IN
		LET tmp = IF (b <= (-51671859296035082003009081632325555741659787529994984020698119751089555379217808850188459572488338859634657790792842594800899821673715919265417497408091589897525887067141545430376776557135939677619872963035609213240007899239253102559232)) THEN ((-1) * (a * (t * ((b * z) - (y2 * y5))))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if b < -5.1671859296035082e235

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(x \cdot \left(y1 \cdot y2\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto a \cdot \left(\mathsf{fma}\left(-1, x \cdot \left(y1 \cdot y2\right), b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]

   8. Taylor expanded in t around -inf

      \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 25.7%

       \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right) \]

   if -5.1671859296035082e235 < b < -1.3375700603832583e50 or 2.2334548789450462e118 < b

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

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

   if -1.3375700603832583e50 < b < 1.6115288797132272e-212

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

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

   if 1.6115288797132272e-212 < b < 2.2334548789450462e118

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

Alternative 20: 33.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;b \leq -5.167185929603508 \cdot 10^{+235}:\\ \;\;\;\;-1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)\\ \mathbf{elif}\;b \leq -1.0463113606232442 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.2398981643199252 \cdot 10^{-306}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 2.124142650588702 \cdot 10^{-212}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 2.233454878945046 \cdot 10^{+118}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \mathsf{fma}\left(-1, c \cdot z, j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* j (* b (- (* t y4) (* x y0))))))
  (if (<= b -5.167185929603508e+235)
    (* -1.0 (* a (* t (- (* b z) (* y2 y5)))))
    (if (<= b -1.0463113606232442e+37)
      t_1
      (if (<= b -2.2398981643199252e-306)
        (* y4 (* c (- (* y y3) (* t y2))))
        (if (<= b 2.124142650588702e-212)
          (* y2 (fma k (- (* y1 y4) (* y0 y5)) (* x (* c y0))))
          (if (<= b 2.233454878945046e+118)
            (* y0 (* y3 (fma -1.0 (* c z) (* j y5))))
            t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -5.167185929603508e+235) {
		tmp = -1.0 * (a * (t * ((b * z) - (y2 * y5))));
	} else if (b <= -1.0463113606232442e+37) {
		tmp = t_1;
	} else if (b <= -2.2398981643199252e-306) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 2.124142650588702e-212) {
		tmp = y2 * fma(k, ((y1 * y4) - (y0 * y5)), (x * (c * y0)));
	} else if (b <= 2.233454878945046e+118) {
		tmp = y0 * (y3 * fma(-1.0, (c * z), (j * y5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (b <= -5.167185929603508e+235)
		tmp = Float64(-1.0 * Float64(a * Float64(t * Float64(Float64(b * z) - Float64(y2 * y5)))));
	elseif (b <= -1.0463113606232442e+37)
		tmp = t_1;
	elseif (b <= -2.2398981643199252e-306)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (b <= 2.124142650588702e-212)
		tmp = Float64(y2 * fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(x * Float64(c * y0))));
	elseif (b <= 2.233454878945046e+118)
		tmp = Float64(y0 * Float64(y3 * fma(-1.0, Float64(c * z), Float64(j * y5))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.167185929603508e+235], N[(-1.0 * N[(a * N[(t * N[(N[(b * z), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.0463113606232442e+37], t$95$1, If[LessEqual[b, -2.2398981643199252e-306], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.124142650588702e-212], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(x * N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.233454878945046e+118], N[(y0 * N[(y3 * N[(-1.0 * N[(c * z), $MachinePrecision] + N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (j * (b * ((t * y4) - (x * y0)))) IN
		LET tmp_4 = IF (b <= (22334548789450461643509347306614627765585692681114701528267652296617185768127828575377205654093831683498965211350564864)) THEN (y0 * (y3 * (((-1) * (c * z)) + (j * y5)))) ELSE t_1 ENDIF IN
		LET tmp_3 = IF (b <= (2124142650588702013681229686389685475758800761822116334786355767658577047315543220695515018415668609082102513506490085590210626431568019088523570188195032207540807739829835280862444325908072101516118153659635885352492762612661743057410532236747700405663175959002746974734222558680266232359840663945306267317250018169965101340903969554994484387097794452567832571229974748011163539446633933837017617636051362800124484984480043631813736450196888109478513052684207529428439834748121180701841187089605361465634303375082936327089555561542510986328125e-755)) THEN (y2 * ((k * ((y1 * y4) - (y0 * y5))) + (x * (c * y0)))) ELSE tmp_4 ENDIF IN
		LET tmp_2 = IF (b <= (-22398981643199252237386139655870323685479046003871429065903114878735748711859813710866802411934400932692082333101812344821330257939836121916830800775316831674216768083352111066938127734184380765146029410803601905127955416393712921319605349525856616086795809365325435767501341405026226203205634705602035138998565524320435900175013313610349891189232757016644355732298330077152792515228695192331999128730618519543442467537806331240317436544599243000603116354561409291474573014192685354541168331993428207496123521136614240952564252721706544814323256077879950477395329144006339559876635049713276243065189451255778467555909925024641123299505725372045167596323812596319858405892554076181008761045875533053213676688264509157780431103379470414438401348888874053955078125e-1066)) THEN (y4 * (c * ((y * y3) - (t * y2)))) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (b <= (-10463113606232441702441488944583409664)) THEN t_1 ELSE tmp_2 ENDIF IN
		LET tmp = IF (b <= (-51671859296035082003009081632325555741659787529994984020698119751089555379217808850188459572488338859634657790792842594800899821673715919265417497408091589897525887067141545430376776557135939677619872963035609213240007899239253102559232)) THEN ((-1) * (a * (t * ((b * z) - (y2 * y5))))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if b < -5.1671859296035082e235

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(x \cdot \left(y1 \cdot y2\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto a \cdot \left(\mathsf{fma}\left(-1, x \cdot \left(y1 \cdot y2\right), b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]

   8. Taylor expanded in t around -inf

      \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 25.7%

       \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right) \]

   if -5.1671859296035082e235 < b < -1.0463113606232442e37 or 2.2334548789450462e118 < b

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

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

   if -1.0463113606232442e37 < b < -2.2398981643199252e-306

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in c around inf

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.5%

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]

   if -2.2398981643199252e-306 < b < 2.124142650588702e-212

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

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

   8. Taylor expanded in a around 0

      \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 32.1%

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

   if 2.124142650588702e-212 < b < 2.2334548789450462e118

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

Alternative 21: 33.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;b \leq -5.167185929603508 \cdot 10^{+235}:\\ \;\;\;\;-1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)\\ \mathbf{elif}\;b \leq -1.0463113606232442 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.922756054437859 \cdot 10^{-295}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 5.976911578218816 \cdot 10^{-230}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.233454878945046 \cdot 10^{+118}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \mathsf{fma}\left(-1, c \cdot z, j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* j (* b (- (* t y4) (* x y0))))))
  (if (<= b -5.167185929603508e+235)
    (* -1.0 (* a (* t (- (* b z) (* y2 y5)))))
    (if (<= b -1.0463113606232442e+37)
      t_1
      (if (<= b -8.922756054437859e-295)
        (* y4 (* c (- (* y y3) (* t y2))))
        (if (<= b 5.976911578218816e-230)
          (* a (* y3 (- (* y1 z) (* y y5))))
          (if (<= b 2.233454878945046e+118)
            (* y0 (* y3 (fma -1.0 (* c z) (* j y5))))
            t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -5.167185929603508e+235) {
		tmp = -1.0 * (a * (t * ((b * z) - (y2 * y5))));
	} else if (b <= -1.0463113606232442e+37) {
		tmp = t_1;
	} else if (b <= -8.922756054437859e-295) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 5.976911578218816e-230) {
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	} else if (b <= 2.233454878945046e+118) {
		tmp = y0 * (y3 * fma(-1.0, (c * z), (j * y5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (b <= -5.167185929603508e+235)
		tmp = Float64(-1.0 * Float64(a * Float64(t * Float64(Float64(b * z) - Float64(y2 * y5)))));
	elseif (b <= -1.0463113606232442e+37)
		tmp = t_1;
	elseif (b <= -8.922756054437859e-295)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (b <= 5.976911578218816e-230)
		tmp = Float64(a * Float64(y3 * Float64(Float64(y1 * z) - Float64(y * y5))));
	elseif (b <= 2.233454878945046e+118)
		tmp = Float64(y0 * Float64(y3 * fma(-1.0, Float64(c * z), Float64(j * y5))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.167185929603508e+235], N[(-1.0 * N[(a * N[(t * N[(N[(b * z), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.0463113606232442e+37], t$95$1, If[LessEqual[b, -8.922756054437859e-295], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.976911578218816e-230], N[(a * N[(y3 * N[(N[(y1 * z), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.233454878945046e+118], N[(y0 * N[(y3 * N[(-1.0 * N[(c * z), $MachinePrecision] + N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (j * (b * ((t * y4) - (x * y0)))) IN
		LET tmp_4 = IF (b <= (22334548789450461643509347306614627765585692681114701528267652296617185768127828575377205654093831683498965211350564864)) THEN (y0 * (y3 * (((-1) * (c * z)) + (j * y5)))) ELSE t_1 ENDIF IN
		LET tmp_3 = IF (b <= (597691157821881578834327986782979030872277930730887416182636644453410880259410207756952926587335430321943601555739644131573542826189152492999951617982785410760165635551267106467796568919099906897176573898893839262300346562219368823398490458484055023921710025556245273234972008053747117180714178052676866558776459717950514328505929782863453436865947907735314482893683130936971570477226367874278992774300103770902853599662711772425441880122353935951883839086501973964872763522686513957482455274144800157866548011266971556575236592573926290108987137428275815409506321884691715240478515625e-814)) THEN (a * (y3 * ((y1 * z) - (y * y5)))) ELSE tmp_4 ENDIF IN
		LET tmp_2 = IF (b <= (-892275605443785860199556409822540664203793384923824804242068150890455951618128106395146978470018935509285785878214907342524814162569531014759997375362074031214808753626123719717786874168537707958304307463122091044273391960423581900254604602924159515174390209616567955153621770210595411451680680395752273212636827629149731407006753782532888003659805789680738958767252763791816713662856532925407446722271893885007912226994144204857046703239729979330989322188585267855858963811806468026074938943267406614001959290594135612956342935438250179273974573765800631091619048351933546348140795251028622181987004805005830669053787563658566308740481217338629037580801220683711227140596821601183897070032617800106056193953918409533798694610595703125e-1029)) THEN (y4 * (c * ((y * y3) - (t * y2)))) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (b <= (-10463113606232441702441488944583409664)) THEN t_1 ELSE tmp_2 ENDIF IN
		LET tmp = IF (b <= (-51671859296035082003009081632325555741659787529994984020698119751089555379217808850188459572488338859634657790792842594800899821673715919265417497408091589897525887067141545430376776557135939677619872963035609213240007899239253102559232)) THEN ((-1) * (a * (t * ((b * z) - (y2 * y5))))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if b < -5.1671859296035082e235

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(x \cdot \left(y1 \cdot y2\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto a \cdot \left(\mathsf{fma}\left(-1, x \cdot \left(y1 \cdot y2\right), b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]

   8. Taylor expanded in t around -inf

      \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 25.7%

       \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right) \]

   if -5.1671859296035082e235 < b < -1.0463113606232442e37 or 2.2334548789450462e118 < b

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

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

   if -1.0463113606232442e37 < b < -8.9227560544378586e-295

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in c around inf

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.5%

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]

   if -8.9227560544378586e-295 < b < 5.9769115782188158e-230

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

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

   7. Applied rewrites 26.7%

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

   if 5.9769115782188158e-230 < b < 2.2334548789450462e118

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

Alternative 22: 32.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;b \leq -1.0463113606232442 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.922756054437859 \cdot 10^{-295}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 5.976911578218816 \cdot 10^{-230}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.233454878945046 \cdot 10^{+118}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \mathsf{fma}\left(-1, c \cdot z, j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* j (* b (- (* t y4) (* x y0))))))
  (if (<= b -1.0463113606232442e+37)
    t_1
    (if (<= b -8.922756054437859e-295)
      (* y4 (* c (- (* y y3) (* t y2))))
      (if (<= b 5.976911578218816e-230)
        (* a (* y3 (- (* y1 z) (* y y5))))
        (if (<= b 2.233454878945046e+118)
          (* y0 (* y3 (fma -1.0 (* c z) (* j y5))))
          t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -1.0463113606232442e+37) {
		tmp = t_1;
	} else if (b <= -8.922756054437859e-295) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 5.976911578218816e-230) {
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	} else if (b <= 2.233454878945046e+118) {
		tmp = y0 * (y3 * fma(-1.0, (c * z), (j * y5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (b <= -1.0463113606232442e+37)
		tmp = t_1;
	elseif (b <= -8.922756054437859e-295)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (b <= 5.976911578218816e-230)
		tmp = Float64(a * Float64(y3 * Float64(Float64(y1 * z) - Float64(y * y5))));
	elseif (b <= 2.233454878945046e+118)
		tmp = Float64(y0 * Float64(y3 * fma(-1.0, Float64(c * z), Float64(j * y5))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.0463113606232442e+37], t$95$1, If[LessEqual[b, -8.922756054437859e-295], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.976911578218816e-230], N[(a * N[(y3 * N[(N[(y1 * z), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.233454878945046e+118], N[(y0 * N[(y3 * N[(-1.0 * N[(c * z), $MachinePrecision] + N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (j * (b * ((t * y4) - (x * y0)))) IN
		LET tmp_3 = IF (b <= (22334548789450461643509347306614627765585692681114701528267652296617185768127828575377205654093831683498965211350564864)) THEN (y0 * (y3 * (((-1) * (c * z)) + (j * y5)))) ELSE t_1 ENDIF IN
		LET tmp_2 = IF (b <= (597691157821881578834327986782979030872277930730887416182636644453410880259410207756952926587335430321943601555739644131573542826189152492999951617982785410760165635551267106467796568919099906897176573898893839262300346562219368823398490458484055023921710025556245273234972008053747117180714178052676866558776459717950514328505929782863453436865947907735314482893683130936971570477226367874278992774300103770902853599662711772425441880122353935951883839086501973964872763522686513957482455274144800157866548011266971556575236592573926290108987137428275815409506321884691715240478515625e-814)) THEN (a * (y3 * ((y1 * z) - (y * y5)))) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (b <= (-892275605443785860199556409822540664203793384923824804242068150890455951618128106395146978470018935509285785878214907342524814162569531014759997375362074031214808753626123719717786874168537707958304307463122091044273391960423581900254604602924159515174390209616567955153621770210595411451680680395752273212636827629149731407006753782532888003659805789680738958767252763791816713662856532925407446722271893885007912226994144204857046703239729979330989322188585267855858963811806468026074938943267406614001959290594135612956342935438250179273974573765800631091619048351933546348140795251028622181987004805005830669053787563658566308740481217338629037580801220683711227140596821601183897070032617800106056193953918409533798694610595703125e-1029)) THEN (y4 * (c * ((y * y3) - (t * y2)))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (b <= (-10463113606232441702441488944583409664)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if b < -1.0463113606232442e37 or 2.2334548789450462e118 < b

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

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

   if -1.0463113606232442e37 < b < -8.9227560544378586e-295

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in c around inf

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.5%

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]

   if -8.9227560544378586e-295 < b < 5.9769115782188158e-230

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

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

   7. Applied rewrites 26.7%

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

   if 5.9769115782188158e-230 < b < 2.2334548789450462e118

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

Alternative 23: 32.5% accurate, 4.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y5 \leq -4.28157968010063 \cdot 10^{+192}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -27964318.70792856:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)\\ \mathbf{elif}\;y5 \leq -1.4311228481909235 \cdot 10^{-59}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 3.468418237697642 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= y5 -4.28157968010063e+192)
  (* y (* y5 (- (* i k) (* a y3))))
  (if (<= y5 -27964318.70792856)
    (* j (* y0 (- (* y3 y5) (* b x))))
    (if (<= y5 -1.4311228481909235e-59)
      (* y4 (* c (- (* y y3) (* t y2))))
      (if (<= y5 3.468418237697642e-36)
        (* j (* b (- (* t y4) (* x y0))))
        (* a (* y5 (- (* t y2) (* y y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -4.28157968010063e+192) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -27964318.70792856) {
		tmp = j * (y0 * ((y3 * y5) - (b * x)));
	} else if (y5 <= -1.4311228481909235e-59) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (y5 <= 3.468418237697642e-36) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-4.28157968010063d+192)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y5 <= (-27964318.70792856d0)) then
        tmp = j * (y0 * ((y3 * y5) - (b * x)))
    else if (y5 <= (-1.4311228481909235d-59)) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else if (y5 <= 3.468418237697642d-36) then
        tmp = j * (b * ((t * y4) - (x * y0)))
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -4.28157968010063e+192) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -27964318.70792856) {
		tmp = j * (y0 * ((y3 * y5) - (b * x)));
	} else if (y5 <= -1.4311228481909235e-59) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (y5 <= 3.468418237697642e-36) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -4.28157968010063e+192:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y5 <= -27964318.70792856:
		tmp = j * (y0 * ((y3 * y5) - (b * x)))
	elif y5 <= -1.4311228481909235e-59:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	elif y5 <= 3.468418237697642e-36:
		tmp = j * (b * ((t * y4) - (x * y0)))
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -4.28157968010063e+192)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y5 <= -27964318.70792856)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(b * x))));
	elseif (y5 <= -1.4311228481909235e-59)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y5 <= 3.468418237697642e-36)
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -4.28157968010063e+192)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y5 <= -27964318.70792856)
		tmp = j * (y0 * ((y3 * y5) - (b * x)));
	elseif (y5 <= -1.4311228481909235e-59)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	elseif (y5 <= 3.468418237697642e-36)
		tmp = j * (b * ((t * y4) - (x * y0)));
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -4.28157968010063e+192], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -27964318.70792856], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(b * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.4311228481909235e-59], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.468418237697642e-36], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_3 = IF (y5 <= (3468418237697642095487415756037247673849058649776573039658362255641878229476602749079060077075364887377872946672141551971435546875e-165)) THEN (j * (b * ((t * y4) - (x * y0)))) ELSE (a * (y5 * ((t * y2) - (y * y3)))) ENDIF IN
	LET tmp_2 = IF (y5 <= (-1431122848190923475640769316702534409054735936425554746501446269393139745798857105259191110599988656838918012796733203376513816643770377815910423082053359866705477543291635811328887939453125e-248)) THEN (y4 * (c * ((y * y3) - (t * y2)))) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (y5 <= (-27964318707928560674190521240234375e-27)) THEN (j * (y0 * ((y3 * y5) - (b * x)))) ELSE tmp_2 ENDIF IN
	LET tmp = IF (y5 <= (-4281579680100630051239483396422248412493485379395880716093578506856050656338194127129414577055577866705315977312061338286449912651610644023873029490418786388705487161793833525158450521631096832)) THEN (y * (y5 * ((i * k) - (a * y3)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if y5 < -4.2815796801006301e192

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]

   if -4.2815796801006301e192 < y5 < -27964318.707928561

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in y0 around inf

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

   7. Applied rewrites 26.8%

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

   if -27964318.707928561 < y5 < -1.4311228481909235e-59

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in c around inf

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.5%

      \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]

   if -1.4311228481909235e-59 < y5 < 3.4684182376976421e-36

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

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

   if 3.4684182376976421e-36 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 24: 32.3% accurate, 4.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y5 \leq -1.89441244634971 \cdot 10^{+189}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -1.5881949173963176 \cdot 10^{-23}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{elif}\;y5 \leq 1.4537788065458614 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 3.468418237697642 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= y5 -1.89441244634971e+189)
  (* y (* y5 (- (* i k) (* a y3))))
  (if (<= y5 -1.5881949173963176e-23)
    (* y0 (* c (- (* x y2) (* y3 z))))
    (if (<= y5 1.4537788065458614e-241)
      (* t (* y4 (- (* b j) (* c y2))))
      (if (<= y5 3.468418237697642e-36)
        (* j (* b (- (* t y4) (* x y0))))
        (* a (* y5 (- (* t y2) (* y y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.89441244634971e+189) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -1.5881949173963176e-23) {
		tmp = y0 * (c * ((x * y2) - (y3 * z)));
	} else if (y5 <= 1.4537788065458614e-241) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y5 <= 3.468418237697642e-36) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-1.89441244634971d+189)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y5 <= (-1.5881949173963176d-23)) then
        tmp = y0 * (c * ((x * y2) - (y3 * z)))
    else if (y5 <= 1.4537788065458614d-241) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (y5 <= 3.468418237697642d-36) then
        tmp = j * (b * ((t * y4) - (x * y0)))
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.89441244634971e+189) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -1.5881949173963176e-23) {
		tmp = y0 * (c * ((x * y2) - (y3 * z)));
	} else if (y5 <= 1.4537788065458614e-241) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y5 <= 3.468418237697642e-36) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -1.89441244634971e+189:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y5 <= -1.5881949173963176e-23:
		tmp = y0 * (c * ((x * y2) - (y3 * z)))
	elif y5 <= 1.4537788065458614e-241:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif y5 <= 3.468418237697642e-36:
		tmp = j * (b * ((t * y4) - (x * y0)))
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -1.89441244634971e+189)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y5 <= -1.5881949173963176e-23)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(y3 * z))));
	elseif (y5 <= 1.4537788065458614e-241)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y5 <= 3.468418237697642e-36)
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -1.89441244634971e+189)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y5 <= -1.5881949173963176e-23)
		tmp = y0 * (c * ((x * y2) - (y3 * z)));
	elseif (y5 <= 1.4537788065458614e-241)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (y5 <= 3.468418237697642e-36)
		tmp = j * (b * ((t * y4) - (x * y0)));
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -1.89441244634971e+189], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.5881949173963176e-23], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.4537788065458614e-241], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.468418237697642e-36], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_3 = IF (y5 <= (3468418237697642095487415756037247673849058649776573039658362255641878229476602749079060077075364887377872946672141551971435546875e-165)) THEN (j * (b * ((t * y4) - (x * y0)))) ELSE (a * (y5 * ((t * y2) - (y * y3)))) ENDIF IN
	LET tmp_2 = IF (y5 <= (145377880654586144605913231258476355089090268182303758105200782268671360987174086225162370586826833752858490020571397310863886905712343834906794282373125931677178692574702157330106724286196544218424875144932959389885454376945504716914320690255094786382101513542699261576444631796893474210975082401897611106435166969559831130556587320135026771907566740801126416043731777111319839871013698544193937166152039895770080758015772236559995987233590596119160116352973035756894088124004016244510963221200786553982993950694734127515674887343024017894658599648910405581316380299659700436887277419373276643455028533935546875e-852)) THEN (t * (y4 * ((b * j) - (c * y2)))) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (y5 <= (-1588194917396317601402519077144506589100085884793860725904264910059160431643476840690709650516510009765625e-128)) THEN (y0 * (c * ((x * y2) - (y3 * z)))) ELSE tmp_2 ENDIF IN
	LET tmp = IF (y5 <= (-1894412446349710004529950842210167576874930333232284119197483229502383622714795937226584887442123881414584363830900749776544767139117623688961530995349673700522877456494618634363226126548992)) THEN (y * (y5 * ((i * k) - (a * y3)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if y5 < -1.89441244634971e189

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]

   if -1.89441244634971e189 < y5 < -1.5881949173963176e-23

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in y5 around 0

      \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 34.7%

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

   8. Taylor expanded in b around 0

      \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 27.3%

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

   if -1.5881949173963176e-23 < y5 < 1.4537788065458614e-241

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]

   if 1.4537788065458614e-241 < y5 < 3.4684182376976421e-36

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

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

   if 3.4684182376976421e-36 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 25: 32.3% accurate, 4.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y5 \leq -4.28157968010063 \cdot 10^{+192}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -5.470887563744298 \cdot 10^{-15}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)\\ \mathbf{elif}\;y5 \leq 1.4537788065458614 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 3.468418237697642 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= y5 -4.28157968010063e+192)
  (* y (* y5 (- (* i k) (* a y3))))
  (if (<= y5 -5.470887563744298e-15)
    (* j (* y0 (- (* y3 y5) (* b x))))
    (if (<= y5 1.4537788065458614e-241)
      (* t (* y4 (- (* b j) (* c y2))))
      (if (<= y5 3.468418237697642e-36)
        (* j (* b (- (* t y4) (* x y0))))
        (* a (* y5 (- (* t y2) (* y y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -4.28157968010063e+192) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -5.470887563744298e-15) {
		tmp = j * (y0 * ((y3 * y5) - (b * x)));
	} else if (y5 <= 1.4537788065458614e-241) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y5 <= 3.468418237697642e-36) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-4.28157968010063d+192)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y5 <= (-5.470887563744298d-15)) then
        tmp = j * (y0 * ((y3 * y5) - (b * x)))
    else if (y5 <= 1.4537788065458614d-241) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (y5 <= 3.468418237697642d-36) then
        tmp = j * (b * ((t * y4) - (x * y0)))
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -4.28157968010063e+192) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -5.470887563744298e-15) {
		tmp = j * (y0 * ((y3 * y5) - (b * x)));
	} else if (y5 <= 1.4537788065458614e-241) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y5 <= 3.468418237697642e-36) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -4.28157968010063e+192:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y5 <= -5.470887563744298e-15:
		tmp = j * (y0 * ((y3 * y5) - (b * x)))
	elif y5 <= 1.4537788065458614e-241:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif y5 <= 3.468418237697642e-36:
		tmp = j * (b * ((t * y4) - (x * y0)))
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -4.28157968010063e+192)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y5 <= -5.470887563744298e-15)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(b * x))));
	elseif (y5 <= 1.4537788065458614e-241)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y5 <= 3.468418237697642e-36)
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -4.28157968010063e+192)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y5 <= -5.470887563744298e-15)
		tmp = j * (y0 * ((y3 * y5) - (b * x)));
	elseif (y5 <= 1.4537788065458614e-241)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (y5 <= 3.468418237697642e-36)
		tmp = j * (b * ((t * y4) - (x * y0)));
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -4.28157968010063e+192], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -5.470887563744298e-15], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(b * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.4537788065458614e-241], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.468418237697642e-36], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_3 = IF (y5 <= (3468418237697642095487415756037247673849058649776573039658362255641878229476602749079060077075364887377872946672141551971435546875e-165)) THEN (j * (b * ((t * y4) - (x * y0)))) ELSE (a * (y5 * ((t * y2) - (y * y3)))) ENDIF IN
	LET tmp_2 = IF (y5 <= (145377880654586144605913231258476355089090268182303758105200782268671360987174086225162370586826833752858490020571397310863886905712343834906794282373125931677178692574702157330106724286196544218424875144932959389885454376945504716914320690255094786382101513542699261576444631796893474210975082401897611106435166969559831130556587320135026771907566740801126416043731777111319839871013698544193937166152039895770080758015772236559995987233590596119160116352973035756894088124004016244510963221200786553982993950694734127515674887343024017894658599648910405581316380299659700436887277419373276643455028533935546875e-852)) THEN (t * (y4 * ((b * j) - (c * y2)))) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (y5 <= (-54708875637442979995204373833298102394617919673469597086068461067043244838714599609375e-100)) THEN (j * (y0 * ((y3 * y5) - (b * x)))) ELSE tmp_2 ENDIF IN
	LET tmp = IF (y5 <= (-4281579680100630051239483396422248412493485379395880716093578506856050656338194127129414577055577866705315977312061338286449912651610644023873029490418786388705487161793833525158450521631096832)) THEN (y * (y5 * ((i * k) - (a * y3)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if y5 < -4.2815796801006301e192

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]

   if -4.2815796801006301e192 < y5 < -5.470887563744298e-15

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in y0 around inf

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

   7. Applied rewrites 26.8%

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

   if -5.470887563744298e-15 < y5 < 1.4537788065458614e-241

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]

   if 1.4537788065458614e-241 < y5 < 3.4684182376976421e-36

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

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

   if 3.4684182376976421e-36 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 26: 32.2% accurate, 4.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y5 \leq -5.5883190188181465 \cdot 10^{+193}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -8.755501971215284 \cdot 10^{+62}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)\\ \mathbf{elif}\;y5 \leq 1.4537788065458614 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 3.468418237697642 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= y5 -5.5883190188181465e+193)
  (* y (* y5 (- (* i k) (* a y3))))
  (if (<= y5 -8.755501971215284e+62)
    (* b (* y0 (- (* k z) (* j x))))
    (if (<= y5 1.4537788065458614e-241)
      (* t (* y4 (- (* b j) (* c y2))))
      (if (<= y5 3.468418237697642e-36)
        (* j (* b (- (* t y4) (* x y0))))
        (* a (* y5 (- (* t y2) (* y y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -5.5883190188181465e+193) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -8.755501971215284e+62) {
		tmp = b * (y0 * ((k * z) - (j * x)));
	} else if (y5 <= 1.4537788065458614e-241) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y5 <= 3.468418237697642e-36) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-5.5883190188181465d+193)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y5 <= (-8.755501971215284d+62)) then
        tmp = b * (y0 * ((k * z) - (j * x)))
    else if (y5 <= 1.4537788065458614d-241) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (y5 <= 3.468418237697642d-36) then
        tmp = j * (b * ((t * y4) - (x * y0)))
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -5.5883190188181465e+193) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -8.755501971215284e+62) {
		tmp = b * (y0 * ((k * z) - (j * x)));
	} else if (y5 <= 1.4537788065458614e-241) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y5 <= 3.468418237697642e-36) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -5.5883190188181465e+193:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y5 <= -8.755501971215284e+62:
		tmp = b * (y0 * ((k * z) - (j * x)))
	elif y5 <= 1.4537788065458614e-241:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif y5 <= 3.468418237697642e-36:
		tmp = j * (b * ((t * y4) - (x * y0)))
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -5.5883190188181465e+193)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y5 <= -8.755501971215284e+62)
		tmp = Float64(b * Float64(y0 * Float64(Float64(k * z) - Float64(j * x))));
	elseif (y5 <= 1.4537788065458614e-241)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y5 <= 3.468418237697642e-36)
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -5.5883190188181465e+193)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y5 <= -8.755501971215284e+62)
		tmp = b * (y0 * ((k * z) - (j * x)));
	elseif (y5 <= 1.4537788065458614e-241)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (y5 <= 3.468418237697642e-36)
		tmp = j * (b * ((t * y4) - (x * y0)));
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -5.5883190188181465e+193], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -8.755501971215284e+62], N[(b * N[(y0 * N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.4537788065458614e-241], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.468418237697642e-36], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_3 = IF (y5 <= (3468418237697642095487415756037247673849058649776573039658362255641878229476602749079060077075364887377872946672141551971435546875e-165)) THEN (j * (b * ((t * y4) - (x * y0)))) ELSE (a * (y5 * ((t * y2) - (y * y3)))) ENDIF IN
	LET tmp_2 = IF (y5 <= (145377880654586144605913231258476355089090268182303758105200782268671360987174086225162370586826833752858490020571397310863886905712343834906794282373125931677178692574702157330106724286196544218424875144932959389885454376945504716914320690255094786382101513542699261576444631796893474210975082401897611106435166969559831130556587320135026771907566740801126416043731777111319839871013698544193937166152039895770080758015772236559995987233590596119160116352973035756894088124004016244510963221200786553982993950694734127515674887343024017894658599648910405581316380299659700436887277419373276643455028533935546875e-852)) THEN (t * (y4 * ((b * j) - (c * y2)))) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (y5 <= (-875550197121528369508218559181971514461925172675265747549683712)) THEN (b * (y0 * ((k * z) - (j * x)))) ELSE tmp_2 ENDIF IN
	LET tmp = IF (y5 <= (-55883190188181465125584335997432347148428398136779834619443693569799759831211458730883907393285905110531761936138397755001434963725007747150090872161393562398835795741701372659512628675419832320)) THEN (y * (y5 * ((i * k) - (a * y3)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if y5 < -5.5883190188181465e193

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]

   if -5.5883190188181465e193 < y5 < -8.7555019712152837e62

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

      \[\leadsto b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right) \]

   if -8.7555019712152837e62 < y5 < 1.4537788065458614e-241

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]

   if 1.4537788065458614e-241 < y5 < 3.4684182376976421e-36

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

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

   if 3.4684182376976421e-36 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 27: 31.1% accurate, 4.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y5 \leq -5.5883190188181465 \cdot 10^{+193}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -8.755501971215284 \cdot 10^{+62}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)\\ \mathbf{elif}\;y5 \leq 1.9746548673569286 \cdot 10^{-247}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2.981712747135271 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= y5 -5.5883190188181465e+193)
  (* y (* y5 (- (* i k) (* a y3))))
  (if (<= y5 -8.755501971215284e+62)
    (* b (* y0 (- (* k z) (* j x))))
    (if (<= y5 1.9746548673569286e-247)
      (* t (* y4 (- (* b j) (* c y2))))
      (if (<= y5 2.981712747135271e+24)
        (* b (* j (- (* t y4) (* x y0))))
        (* a (* y5 (- (* t y2) (* y y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -5.5883190188181465e+193) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -8.755501971215284e+62) {
		tmp = b * (y0 * ((k * z) - (j * x)));
	} else if (y5 <= 1.9746548673569286e-247) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y5 <= 2.981712747135271e+24) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-5.5883190188181465d+193)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y5 <= (-8.755501971215284d+62)) then
        tmp = b * (y0 * ((k * z) - (j * x)))
    else if (y5 <= 1.9746548673569286d-247) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (y5 <= 2.981712747135271d+24) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -5.5883190188181465e+193) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -8.755501971215284e+62) {
		tmp = b * (y0 * ((k * z) - (j * x)));
	} else if (y5 <= 1.9746548673569286e-247) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y5 <= 2.981712747135271e+24) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -5.5883190188181465e+193:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y5 <= -8.755501971215284e+62:
		tmp = b * (y0 * ((k * z) - (j * x)))
	elif y5 <= 1.9746548673569286e-247:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif y5 <= 2.981712747135271e+24:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -5.5883190188181465e+193)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y5 <= -8.755501971215284e+62)
		tmp = Float64(b * Float64(y0 * Float64(Float64(k * z) - Float64(j * x))));
	elseif (y5 <= 1.9746548673569286e-247)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y5 <= 2.981712747135271e+24)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -5.5883190188181465e+193)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y5 <= -8.755501971215284e+62)
		tmp = b * (y0 * ((k * z) - (j * x)));
	elseif (y5 <= 1.9746548673569286e-247)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (y5 <= 2.981712747135271e+24)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -5.5883190188181465e+193], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -8.755501971215284e+62], N[(b * N[(y0 * N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.9746548673569286e-247], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.981712747135271e+24], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_3 = IF (y5 <= (2981712747135271161561088)) THEN (b * (j * ((t * y4) - (x * y0)))) ELSE (a * (y5 * ((t * y2) - (y * y3)))) ENDIF IN
	LET tmp_2 = IF (y5 <= (19746548673569286092862003130747096356865853889880423839550756865053322640250974839593861627319484925052869068545485576737400277077599119960329174240012428750679624424453918852793085398316796102338546877729172307521486080935232155434258308459368273895709409381729234586559191991841532004534465880597584355192826218572878458397698539765851124939026641760147791977563874146844891031810429081311840336283628018501285786913106527545546686727451013466826411086123926627070720594350902455386122132071538141957815858072686840326778677383721565807885097589776638838481583967818406667055027210212758692620127476402558386325836181640625e-872)) THEN (t * (y4 * ((b * j) - (c * y2)))) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (y5 <= (-875550197121528369508218559181971514461925172675265747549683712)) THEN (b * (y0 * ((k * z) - (j * x)))) ELSE tmp_2 ENDIF IN
	LET tmp = IF (y5 <= (-55883190188181465125584335997432347148428398136779834619443693569799759831211458730883907393285905110531761936138397755001434963725007747150090872161393562398835795741701372659512628675419832320)) THEN (y * (y5 * ((i * k) - (a * y3)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if y5 < -5.5883190188181465e193

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]

   if -5.5883190188181465e193 < y5 < -8.7555019712152837e62

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

      \[\leadsto b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right) \]

   if -8.7555019712152837e62 < y5 < 1.9746548673569286e-247

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]

   if 1.9746548673569286e-247 < y5 < 2.9817127471352712e24

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

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

   if 2.9817127471352712e24 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 28: 30.9% accurate, 3.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y5 \leq -4.28157968010063 \cdot 10^{+192}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -8.942631851008151 \cdot 10^{-147}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;y5 \leq 4.115958861025253 \cdot 10^{-262}:\\ \;\;\;\;\left(\left(-y2 \cdot c\right) \cdot y4\right) \cdot t\\ \mathbf{elif}\;y5 \leq 5.78753494874837 \cdot 10^{-127}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(-j \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 1.9094503604452098 \cdot 10^{-36}:\\ \;\;\;\;y4 \cdot \left(-\left(k \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= y5 -4.28157968010063e+192)
  (* y (* y5 (- (* i k) (* a y3))))
  (if (<= y5 -8.942631851008151e-147)
    (* y3 (* y5 (- (* j y0) (* a y))))
    (if (<= y5 4.115958861025253e-262)
      (* (* (- (* y2 c)) y4) t)
      (if (<= y5 5.78753494874837e-127)
        (* y0 (* x (- (* j b))))
        (if (<= y5 1.9094503604452098e-36)
          (* y4 (- (* (* k y) b)))
          (* a (* y5 (- (* t y2) (* y y3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -4.28157968010063e+192) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -8.942631851008151e-147) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (y5 <= 4.115958861025253e-262) {
		tmp = (-(y2 * c) * y4) * t;
	} else if (y5 <= 5.78753494874837e-127) {
		tmp = y0 * (x * -(j * b));
	} else if (y5 <= 1.9094503604452098e-36) {
		tmp = y4 * -((k * y) * b);
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-4.28157968010063d+192)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y5 <= (-8.942631851008151d-147)) then
        tmp = y3 * (y5 * ((j * y0) - (a * y)))
    else if (y5 <= 4.115958861025253d-262) then
        tmp = (-(y2 * c) * y4) * t
    else if (y5 <= 5.78753494874837d-127) then
        tmp = y0 * (x * -(j * b))
    else if (y5 <= 1.9094503604452098d-36) then
        tmp = y4 * -((k * y) * b)
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -4.28157968010063e+192) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= -8.942631851008151e-147) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (y5 <= 4.115958861025253e-262) {
		tmp = (-(y2 * c) * y4) * t;
	} else if (y5 <= 5.78753494874837e-127) {
		tmp = y0 * (x * -(j * b));
	} else if (y5 <= 1.9094503604452098e-36) {
		tmp = y4 * -((k * y) * b);
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -4.28157968010063e+192:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y5 <= -8.942631851008151e-147:
		tmp = y3 * (y5 * ((j * y0) - (a * y)))
	elif y5 <= 4.115958861025253e-262:
		tmp = (-(y2 * c) * y4) * t
	elif y5 <= 5.78753494874837e-127:
		tmp = y0 * (x * -(j * b))
	elif y5 <= 1.9094503604452098e-36:
		tmp = y4 * -((k * y) * b)
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -4.28157968010063e+192)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y5 <= -8.942631851008151e-147)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (y5 <= 4.115958861025253e-262)
		tmp = Float64(Float64(Float64(-Float64(y2 * c)) * y4) * t);
	elseif (y5 <= 5.78753494874837e-127)
		tmp = Float64(y0 * Float64(x * Float64(-Float64(j * b))));
	elseif (y5 <= 1.9094503604452098e-36)
		tmp = Float64(y4 * Float64(-Float64(Float64(k * y) * b)));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -4.28157968010063e+192)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y5 <= -8.942631851008151e-147)
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	elseif (y5 <= 4.115958861025253e-262)
		tmp = (-(y2 * c) * y4) * t;
	elseif (y5 <= 5.78753494874837e-127)
		tmp = y0 * (x * -(j * b));
	elseif (y5 <= 1.9094503604452098e-36)
		tmp = y4 * -((k * y) * b);
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -4.28157968010063e+192], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -8.942631851008151e-147], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.115958861025253e-262], N[(N[((-N[(y2 * c), $MachinePrecision]) * y4), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y5, 5.78753494874837e-127], N[(y0 * N[(x * (-N[(j * b), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.9094503604452098e-36], N[(y4 * (-N[(N[(k * y), $MachinePrecision] * b), $MachinePrecision])), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_4 = IF (y5 <= (190945036044520977809968900367187994115990586769389504218361471276673213380039066774224347316189775991546184741309843957424163818359375e-170)) THEN (y4 * (- ((k * y) * b))) ELSE (a * (y5 * ((t * y2) - (y * y3)))) ENDIF IN
	LET tmp_3 = IF (y5 <= (5787534948748369908699412907924084249744760906897062456189026638431859990193023994810045238179794461200748654350843149900260238049831184487513167690041432428649969308145550755950938895607286459136401838493460813314839694225212273318039214397053309737199175955147541651890629066636217318169440071730426377628886402959551560343243181705474853515625e-472)) THEN (y0 * (x * (- (j * b)))) ELSE tmp_4 ENDIF IN
	LET tmp_2 = IF (y5 <= (411595886102525315527544067255172433395255551520555174083963067758041230957240192923662982557049797958310462433153471930102487076228868321298856831566499550055032768383095072369565238300768195551716169080393893716463887557961923980677819770960936212365490148435715055564384576309545517064233202098119410419469811509805117410725859477136027920294286942585824120154119214152102471100788534791551271869831990556512141934883159014899382086334944871651372485216513338657300184362588314391314864424054671789659608908963498399024022623809444076525373933693696358014746187733364672528405299368137141396536947268748568001993045663289283453423195169307291507720947265625e-921)) THEN (((- (y2 * c)) * y4) * t) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (y5 <= (-8942631851008151307939033979568996435723686020399439278730688917106297807719854269031049214926391432682070902226971059177042645415175202770136034174346062689346894166845580180063030475497642417600973216374088364865932574947229548485944648612051232371939321076678184803790963075951940347623367179761995369805370869183588658401125677279507304383605469262630283111548123997636139392852783203125e-537)) THEN (y3 * (y5 * ((j * y0) - (a * y)))) ELSE tmp_2 ENDIF IN
	LET tmp = IF (y5 <= (-4281579680100630051239483396422248412493485379395880716093578506856050656338194127129414577055577866705315977312061338286449912651610644023873029490418786388705487161793833525158450521631096832)) THEN (y * (y5 * ((i * k) - (a * y3)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 6 regimes

2. if y5 < -4.2815796801006301e192

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]

   if -4.2815796801006301e192 < y5 < -8.9426318510081513e-147

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y3 around -inf

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

   7. Applied rewrites 26.6%

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

   if -8.9426318510081513e-147 < y5 < 4.1159588610252532e-262

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]

   8. Taylor expanded in b around 0

      \[\leadsto t \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot y2\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.0%

       \[\leadsto t \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot y2\right)\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 17.0%

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

   if 4.1159588610252532e-262 < y5 < 5.7875349487483699e-127

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.4%

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

   8. Taylor expanded in b around inf

      \[\leadsto y0 \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot j\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.0%

       \[\leadsto y0 \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot j\right)\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 17.0%

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

   if 5.7875349487483699e-127 < y5 < 1.9094503604452098e-36

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

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

   7. Applied rewrites 25.9%

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

   8. Taylor expanded in b around inf

      \[\leadsto y4 \cdot \left(-1 \cdot \left(b \cdot \left(k \cdot y\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.3%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(b \cdot \left(k \cdot y\right)\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 17.3%

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

   if 1.9094503604452098e-36 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 29: 28.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y5 \leq -1.656905208329892 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 2.981712747135271 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= y5 -1.656905208329892e+126)
  (* y (* y5 (- (* i k) (* a y3))))
  (if (<= y5 2.981712747135271e+24)
    (* b (* j (- (* t y4) (* x y0))))
    (* a (* y5 (- (* t y2) (* y y3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.656905208329892e+126) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= 2.981712747135271e+24) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-1.656905208329892d+126)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y5 <= 2.981712747135271d+24) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.656905208329892e+126) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y5 <= 2.981712747135271e+24) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -1.656905208329892e+126:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y5 <= 2.981712747135271e+24:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -1.656905208329892e+126)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y5 <= 2.981712747135271e+24)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -1.656905208329892e+126)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y5 <= 2.981712747135271e+24)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -1.656905208329892e+126], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.981712747135271e+24], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_1 = IF (y5 <= (2981712747135271161561088)) THEN (b * (j * ((t * y4) - (x * y0)))) ELSE (a * (y5 * ((t * y2) - (y * y3)))) ENDIF IN
	LET tmp = IF (y5 <= (-1656905208329892070971104755210431180635248394686731355047952596958476523965578881904949601208914744247175104213453619947634688)) THEN (y * (y5 * ((i * k) - (a * y3)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if y5 < -1.6569052083298921e126

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right) \]

   if -1.6569052083298921e126 < y5 < 2.9817127471352712e24

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

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

   if 2.9817127471352712e24 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 30: 26.2% accurate, 5.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;b \leq -8.879616088651221 \cdot 10^{+20}:\\ \;\;\;\;-1 \cdot \left(a \cdot \left(\left(b \cdot t\right) \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 1.3233664324334534 \cdot 10^{-160}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 4.926536564957445 \cdot 10^{+79}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.3800415238720206 \cdot 10^{+146}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(k \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(-j \cdot b\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= b -8.879616088651221e+20)
  (* -1.0 (* a (* (* b t) z)))
  (if (<= b 1.3233664324334534e-160)
    (* a (* y5 (- (* t y2) (* y y3))))
    (if (<= b 4.926536564957445e+79)
      (* j (* y5 (* y0 y3)))
      (if (<= b 3.3800415238720206e+146)
        (* y0 (* b (* k z)))
        (* y0 (* x (- (* j b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -8.879616088651221e+20) {
		tmp = -1.0 * (a * ((b * t) * z));
	} else if (b <= 1.3233664324334534e-160) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (b <= 4.926536564957445e+79) {
		tmp = j * (y5 * (y0 * y3));
	} else if (b <= 3.3800415238720206e+146) {
		tmp = y0 * (b * (k * z));
	} else {
		tmp = y0 * (x * -(j * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-8.879616088651221d+20)) then
        tmp = (-1.0d0) * (a * ((b * t) * z))
    else if (b <= 1.3233664324334534d-160) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (b <= 4.926536564957445d+79) then
        tmp = j * (y5 * (y0 * y3))
    else if (b <= 3.3800415238720206d+146) then
        tmp = y0 * (b * (k * z))
    else
        tmp = y0 * (x * -(j * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -8.879616088651221e+20) {
		tmp = -1.0 * (a * ((b * t) * z));
	} else if (b <= 1.3233664324334534e-160) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (b <= 4.926536564957445e+79) {
		tmp = j * (y5 * (y0 * y3));
	} else if (b <= 3.3800415238720206e+146) {
		tmp = y0 * (b * (k * z));
	} else {
		tmp = y0 * (x * -(j * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -8.879616088651221e+20:
		tmp = -1.0 * (a * ((b * t) * z))
	elif b <= 1.3233664324334534e-160:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif b <= 4.926536564957445e+79:
		tmp = j * (y5 * (y0 * y3))
	elif b <= 3.3800415238720206e+146:
		tmp = y0 * (b * (k * z))
	else:
		tmp = y0 * (x * -(j * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -8.879616088651221e+20)
		tmp = Float64(-1.0 * Float64(a * Float64(Float64(b * t) * z)));
	elseif (b <= 1.3233664324334534e-160)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (b <= 4.926536564957445e+79)
		tmp = Float64(j * Float64(y5 * Float64(y0 * y3)));
	elseif (b <= 3.3800415238720206e+146)
		tmp = Float64(y0 * Float64(b * Float64(k * z)));
	else
		tmp = Float64(y0 * Float64(x * Float64(-Float64(j * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -8.879616088651221e+20)
		tmp = -1.0 * (a * ((b * t) * z));
	elseif (b <= 1.3233664324334534e-160)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (b <= 4.926536564957445e+79)
		tmp = j * (y5 * (y0 * y3));
	elseif (b <= 3.3800415238720206e+146)
		tmp = y0 * (b * (k * z));
	else
		tmp = y0 * (x * -(j * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -8.879616088651221e+20], N[(-1.0 * N[(a * N[(N[(b * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.3233664324334534e-160], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.926536564957445e+79], N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3800415238720206e+146], N[(y0 * N[(b * N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(x * (-N[(j * b), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_3 = IF (b <= (338004152387202056077747892541429447838383475124531563119249778631601955937953267065099976614307541927481224192584606825287680862629544591141896192)) THEN (y0 * (b * (k * z))) ELSE (y0 * (x * (- (j * b)))) ENDIF IN
	LET tmp_2 = IF (b <= (49265365649574449103742562897902513130796967782423437918383501716997297290608640)) THEN (j * (y5 * (y0 * y3))) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (b <= (132336643243345339638317062162698814615735603544183753474110927101097657175634055897180183275236180488347206743164045141791747199377753107313212562769356738157578917191076444772969446708475738274385571263734232692861641490642376717782828999873975065929934925582074010363373938984316050763020212349139851591367293455524936886107358746326607209499273496499843595392504210525461017119129569774571564266807399690151214599609375e-582)) THEN (a * (y5 * ((t * y2) - (y * y3)))) ELSE tmp_2 ENDIF IN
	LET tmp = IF (b <= (-887961608865122091008)) THEN ((-1) * (a * ((b * t) * z))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if b < -887961608865122090000

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(x \cdot \left(y1 \cdot y2\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto a \cdot \left(\mathsf{fma}\left(-1, x \cdot \left(y1 \cdot y2\right), b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.9%

       \[\leadsto -1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 16.8%

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

   if -887961608865122090000 < b < 1.3233664324334534e-160

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   if 1.3233664324334534e-160 < b < 4.9265365649574449e79

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in j around -inf

      \[\leadsto j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.5%

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

   8. Taylor expanded in t around 0

      \[\leadsto j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.9%

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

   if 4.9265365649574449e79 < b < 3.3800415238720206e146

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in b around inf

      \[\leadsto y0 \cdot \left(b \cdot \left(k \cdot z - j \cdot x\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.5%

      \[\leadsto y0 \cdot \left(b \cdot \left(k \cdot z - j \cdot x\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto y0 \cdot \left(b \cdot \left(k \cdot z\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.1%

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

   if 3.3800415238720206e146 < b

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.4%

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

   8. Taylor expanded in b around inf

      \[\leadsto y0 \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot j\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.0%

       \[\leadsto y0 \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot j\right)\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 17.0%

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

Alternative 31: 25.7% accurate, 5.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;b \leq -6.476716673930207 \cdot 10^{+94}:\\ \;\;\;\;-1 \cdot \left(a \cdot \left(\left(b \cdot t\right) \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 8.670372285892853 \cdot 10^{-230}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 4.926536564957445 \cdot 10^{+79}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.3800415238720206 \cdot 10^{+146}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(k \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(-j \cdot b\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= b -6.476716673930207e+94)
  (* -1.0 (* a (* (* b t) z)))
  (if (<= b 8.670372285892853e-230)
    (* a (* y3 (- (* y1 z) (* y y5))))
    (if (<= b 4.926536564957445e+79)
      (* j (* y5 (* y0 y3)))
      (if (<= b 3.3800415238720206e+146)
        (* y0 (* b (* k z)))
        (* y0 (* x (- (* j b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -6.476716673930207e+94) {
		tmp = -1.0 * (a * ((b * t) * z));
	} else if (b <= 8.670372285892853e-230) {
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	} else if (b <= 4.926536564957445e+79) {
		tmp = j * (y5 * (y0 * y3));
	} else if (b <= 3.3800415238720206e+146) {
		tmp = y0 * (b * (k * z));
	} else {
		tmp = y0 * (x * -(j * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-6.476716673930207d+94)) then
        tmp = (-1.0d0) * (a * ((b * t) * z))
    else if (b <= 8.670372285892853d-230) then
        tmp = a * (y3 * ((y1 * z) - (y * y5)))
    else if (b <= 4.926536564957445d+79) then
        tmp = j * (y5 * (y0 * y3))
    else if (b <= 3.3800415238720206d+146) then
        tmp = y0 * (b * (k * z))
    else
        tmp = y0 * (x * -(j * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -6.476716673930207e+94) {
		tmp = -1.0 * (a * ((b * t) * z));
	} else if (b <= 8.670372285892853e-230) {
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	} else if (b <= 4.926536564957445e+79) {
		tmp = j * (y5 * (y0 * y3));
	} else if (b <= 3.3800415238720206e+146) {
		tmp = y0 * (b * (k * z));
	} else {
		tmp = y0 * (x * -(j * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -6.476716673930207e+94:
		tmp = -1.0 * (a * ((b * t) * z))
	elif b <= 8.670372285892853e-230:
		tmp = a * (y3 * ((y1 * z) - (y * y5)))
	elif b <= 4.926536564957445e+79:
		tmp = j * (y5 * (y0 * y3))
	elif b <= 3.3800415238720206e+146:
		tmp = y0 * (b * (k * z))
	else:
		tmp = y0 * (x * -(j * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -6.476716673930207e+94)
		tmp = Float64(-1.0 * Float64(a * Float64(Float64(b * t) * z)));
	elseif (b <= 8.670372285892853e-230)
		tmp = Float64(a * Float64(y3 * Float64(Float64(y1 * z) - Float64(y * y5))));
	elseif (b <= 4.926536564957445e+79)
		tmp = Float64(j * Float64(y5 * Float64(y0 * y3)));
	elseif (b <= 3.3800415238720206e+146)
		tmp = Float64(y0 * Float64(b * Float64(k * z)));
	else
		tmp = Float64(y0 * Float64(x * Float64(-Float64(j * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -6.476716673930207e+94)
		tmp = -1.0 * (a * ((b * t) * z));
	elseif (b <= 8.670372285892853e-230)
		tmp = a * (y3 * ((y1 * z) - (y * y5)));
	elseif (b <= 4.926536564957445e+79)
		tmp = j * (y5 * (y0 * y3));
	elseif (b <= 3.3800415238720206e+146)
		tmp = y0 * (b * (k * z));
	else
		tmp = y0 * (x * -(j * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -6.476716673930207e+94], N[(-1.0 * N[(a * N[(N[(b * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.670372285892853e-230], N[(a * N[(y3 * N[(N[(y1 * z), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.926536564957445e+79], N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3800415238720206e+146], N[(y0 * N[(b * N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(x * (-N[(j * b), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_3 = IF (b <= (338004152387202056077747892541429447838383475124531563119249778631601955937953267065099976614307541927481224192584606825287680862629544591141896192)) THEN (y0 * (b * (k * z))) ELSE (y0 * (x * (- (j * b)))) ENDIF IN
	LET tmp_2 = IF (b <= (49265365649574449103742562897902513130796967782423437918383501716997297290608640)) THEN (j * (y5 * (y0 * y3))) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (b <= (86703722858928528047144197903365636773761532783952808465570248487892518654475476866302937663613093961421565356534999597711884748347616554282450048194408302006440404649989696303210237540903782218505844900818808309694671309259646935056731743710717105034197076190860713305946097090691452030923480960652644128776028359055643609868389000540589739488372708417316612826363496674128047325315205027131667876162488800511347502864439383388524437375750066637579838526503948183910875438692881596778836064749380273570176004110411445492517466101130605183613074549153765246956027112901210784912109375e-813)) THEN (a * (y3 * ((y1 * z) - (y * y5)))) ELSE tmp_2 ENDIF IN
	LET tmp = IF (b <= (-64767166739302073429711010011102665731906239375262399010530799726608012823336782705646853160960)) THEN ((-1) * (a * ((b * t) * z))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if b < -6.4767166739302073e94

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around 0

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(\left(-1 \cdot \left(x \cdot \left(y1 \cdot y2\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto a \cdot \left(\mathsf{fma}\left(-1, x \cdot \left(y1 \cdot y2\right), b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.9%

       \[\leadsto -1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 16.8%

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

   if -6.4767166739302073e94 < b < 8.6703722858928528e-230

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

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

   7. Applied rewrites 26.7%

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

   if 8.6703722858928528e-230 < b < 4.9265365649574449e79

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in j around -inf

      \[\leadsto j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.5%

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

   8. Taylor expanded in t around 0

      \[\leadsto j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.9%

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

   if 4.9265365649574449e79 < b < 3.3800415238720206e146

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in b around inf

      \[\leadsto y0 \cdot \left(b \cdot \left(k \cdot z - j \cdot x\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.5%

      \[\leadsto y0 \cdot \left(b \cdot \left(k \cdot z - j \cdot x\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto y0 \cdot \left(b \cdot \left(k \cdot z\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.1%

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

   if 3.3800415238720206e146 < b

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.4%

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

   8. Taylor expanded in b around inf

      \[\leadsto y0 \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot j\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.0%

       \[\leadsto y0 \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot j\right)\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 17.0%

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

Alternative 32: 22.8% accurate, 4.5× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -1.5800475277928215 \cdot 10^{+189}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y\right) \cdot y5\right)\\ \mathbf{elif}\;y5 \leq -2.82939017794136 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 4.115958861025253 \cdot 10^{-262}:\\ \;\;\;\;\left(\left(-y2 \cdot c\right) \cdot y4\right) \cdot t\\ \mathbf{elif}\;y5 \leq 5.78753494874837 \cdot 10^{-127}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(-j \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 7.31818993521813 \cdot 10^{-24}:\\ \;\;\;\;y4 \cdot \left(-\left(k \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* j (* y0 (* y3 y5)))))
  (if (<= y5 -1.5800475277928215e+189)
    (* k (* (* i y) y5))
    (if (<= y5 -2.82939017794136e+50)
      t_1
      (if (<= y5 4.115958861025253e-262)
        (* (* (- (* y2 c)) y4) t)
        (if (<= y5 5.78753494874837e-127)
          (* y0 (* x (- (* j b))))
          (if (<= y5 7.31818993521813e-24)
            (* y4 (- (* (* k y) b)))
            t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y0 * (y3 * y5));
	double tmp;
	if (y5 <= -1.5800475277928215e+189) {
		tmp = k * ((i * y) * y5);
	} else if (y5 <= -2.82939017794136e+50) {
		tmp = t_1;
	} else if (y5 <= 4.115958861025253e-262) {
		tmp = (-(y2 * c) * y4) * t;
	} else if (y5 <= 5.78753494874837e-127) {
		tmp = y0 * (x * -(j * b));
	} else if (y5 <= 7.31818993521813e-24) {
		tmp = y4 * -((k * y) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (y0 * (y3 * y5))
    if (y5 <= (-1.5800475277928215d+189)) then
        tmp = k * ((i * y) * y5)
    else if (y5 <= (-2.82939017794136d+50)) then
        tmp = t_1
    else if (y5 <= 4.115958861025253d-262) then
        tmp = (-(y2 * c) * y4) * t
    else if (y5 <= 5.78753494874837d-127) then
        tmp = y0 * (x * -(j * b))
    else if (y5 <= 7.31818993521813d-24) then
        tmp = y4 * -((k * y) * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y0 * (y3 * y5));
	double tmp;
	if (y5 <= -1.5800475277928215e+189) {
		tmp = k * ((i * y) * y5);
	} else if (y5 <= -2.82939017794136e+50) {
		tmp = t_1;
	} else if (y5 <= 4.115958861025253e-262) {
		tmp = (-(y2 * c) * y4) * t;
	} else if (y5 <= 5.78753494874837e-127) {
		tmp = y0 * (x * -(j * b));
	} else if (y5 <= 7.31818993521813e-24) {
		tmp = y4 * -((k * y) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y0 * (y3 * y5))
	tmp = 0
	if y5 <= -1.5800475277928215e+189:
		tmp = k * ((i * y) * y5)
	elif y5 <= -2.82939017794136e+50:
		tmp = t_1
	elif y5 <= 4.115958861025253e-262:
		tmp = (-(y2 * c) * y4) * t
	elif y5 <= 5.78753494874837e-127:
		tmp = y0 * (x * -(j * b))
	elif y5 <= 7.31818993521813e-24:
		tmp = y4 * -((k * y) * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y0 * Float64(y3 * y5)))
	tmp = 0.0
	if (y5 <= -1.5800475277928215e+189)
		tmp = Float64(k * Float64(Float64(i * y) * y5));
	elseif (y5 <= -2.82939017794136e+50)
		tmp = t_1;
	elseif (y5 <= 4.115958861025253e-262)
		tmp = Float64(Float64(Float64(-Float64(y2 * c)) * y4) * t);
	elseif (y5 <= 5.78753494874837e-127)
		tmp = Float64(y0 * Float64(x * Float64(-Float64(j * b))));
	elseif (y5 <= 7.31818993521813e-24)
		tmp = Float64(y4 * Float64(-Float64(Float64(k * y) * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (y0 * (y3 * y5));
	tmp = 0.0;
	if (y5 <= -1.5800475277928215e+189)
		tmp = k * ((i * y) * y5);
	elseif (y5 <= -2.82939017794136e+50)
		tmp = t_1;
	elseif (y5 <= 4.115958861025253e-262)
		tmp = (-(y2 * c) * y4) * t;
	elseif (y5 <= 5.78753494874837e-127)
		tmp = y0 * (x * -(j * b));
	elseif (y5 <= 7.31818993521813e-24)
		tmp = y4 * -((k * y) * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.5800475277928215e+189], N[(k * N[(N[(i * y), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.82939017794136e+50], t$95$1, If[LessEqual[y5, 4.115958861025253e-262], N[(N[((-N[(y2 * c), $MachinePrecision]) * y4), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y5, 5.78753494874837e-127], N[(y0 * N[(x * (-N[(j * b), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7.31818993521813e-24], N[(y4 * (-N[(N[(k * y), $MachinePrecision] * b), $MachinePrecision])), $MachinePrecision], t$95$1]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (j * (y0 * (y3 * y5))) IN
		LET tmp_4 = IF (y5 <= (7318189935218129715622944333285729130298350258178333730281259054441245215372191523783840239048004150390625e-129)) THEN (y4 * (- ((k * y) * b))) ELSE t_1 ENDIF IN
		LET tmp_3 = IF (y5 <= (5787534948748369908699412907924084249744760906897062456189026638431859990193023994810045238179794461200748654350843149900260238049831184487513167690041432428649969308145550755950938895607286459136401838493460813314839694225212273318039214397053309737199175955147541651890629066636217318169440071730426377628886402959551560343243181705474853515625e-472)) THEN (y0 * (x * (- (j * b)))) ELSE tmp_4 ENDIF IN
		LET tmp_2 = IF (y5 <= (411595886102525315527544067255172433395255551520555174083963067758041230957240192923662982557049797958310462433153471930102487076228868321298856831566499550055032768383095072369565238300768195551716169080393893716463887557961923980677819770960936212365490148435715055564384576309545517064233202098119410419469811509805117410725859477136027920294286942585824120154119214152102471100788534791551271869831990556512141934883159014899382086334944871651372485216513338657300184362588314391314864424054671789659608908963498399024022623809444076525373933693696358014746187733364672528405299368137141396536947268748568001993045663289283453423195169307291507720947265625e-921)) THEN (((- (y2 * c)) * y4) * t) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (y5 <= (-282939017794136019768778887573958489561264807739392)) THEN t_1 ELSE tmp_2 ENDIF IN
		LET tmp = IF (y5 <= (-1580047527792821508643324012569263285441376655464830329581682644176629442742749411117031682488271577633271751776168801701621061354015935631401221876714727786113253247273803210073196961202176)) THEN (k * ((i * y) * y5)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if y5 < -1.5800475277928215e189

   1. Initial program 29.3%

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

   2. Taylor expanded in k around inf

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

   4. Applied rewrites 36.7%

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

   5. Taylor expanded in i around inf

      \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.5%

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

   8. Taylor expanded in y around inf

      \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.6%

       \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 17.6%

       \[\leadsto k \cdot \left(\left(i \cdot y\right) \cdot y5\right) \]

   if -1.5800475277928215e189 < y5 < -2.8293901779413602e50 or 7.3181899352181297e-24 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in y0 around inf

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

   7. Applied rewrites 26.8%

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

   8. Taylor expanded in x around 0

      \[\leadsto j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.8%

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

   if -2.8293901779413602e50 < y5 < 4.1159588610252532e-262

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]

   8. Taylor expanded in b around 0

      \[\leadsto t \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot y2\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.0%

       \[\leadsto t \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot y2\right)\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 17.0%

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

   if 4.1159588610252532e-262 < y5 < 5.7875349487483699e-127

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.4%

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

   8. Taylor expanded in b around inf

      \[\leadsto y0 \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot j\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.0%

       \[\leadsto y0 \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot j\right)\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 17.0%

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

   if 5.7875349487483699e-127 < y5 < 7.3181899352181297e-24

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y around -inf

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

   7. Applied rewrites 25.9%

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

   8. Taylor expanded in b around inf

      \[\leadsto y4 \cdot \left(-1 \cdot \left(b \cdot \left(k \cdot y\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.3%

       \[\leadsto y4 \cdot \left(-1 \cdot \left(b \cdot \left(k \cdot y\right)\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 17.3%

       \[\leadsto y4 \cdot \left(-\left(k \cdot y\right) \cdot b\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 33: 22.7% accurate, 4.7× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -1.5800475277928215 \cdot 10^{+189}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y\right) \cdot y5\right)\\ \mathbf{elif}\;y5 \leq -2.82939017794136 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 4.115958861025253 \cdot 10^{-262}:\\ \;\;\;\;\left(\left(-y2 \cdot c\right) \cdot y4\right) \cdot t\\ \mathbf{elif}\;y5 \leq 1.3569357484949191 \cdot 10^{-134}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(-j \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 6.127283204794414 \cdot 10^{+81}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* j (* y0 (* y3 y5)))))
  (if (<= y5 -1.5800475277928215e+189)
    (* k (* (* i y) y5))
    (if (<= y5 -2.82939017794136e+50)
      t_1
      (if (<= y5 4.115958861025253e-262)
        (* (* (- (* y2 c)) y4) t)
        (if (<= y5 1.3569357484949191e-134)
          (* y0 (* x (- (* j b))))
          (if (<= y5 6.127283204794414e+81)
            (* y2 (* k (* y1 y4)))
            t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y0 * (y3 * y5));
	double tmp;
	if (y5 <= -1.5800475277928215e+189) {
		tmp = k * ((i * y) * y5);
	} else if (y5 <= -2.82939017794136e+50) {
		tmp = t_1;
	} else if (y5 <= 4.115958861025253e-262) {
		tmp = (-(y2 * c) * y4) * t;
	} else if (y5 <= 1.3569357484949191e-134) {
		tmp = y0 * (x * -(j * b));
	} else if (y5 <= 6.127283204794414e+81) {
		tmp = y2 * (k * (y1 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (y0 * (y3 * y5))
    if (y5 <= (-1.5800475277928215d+189)) then
        tmp = k * ((i * y) * y5)
    else if (y5 <= (-2.82939017794136d+50)) then
        tmp = t_1
    else if (y5 <= 4.115958861025253d-262) then
        tmp = (-(y2 * c) * y4) * t
    else if (y5 <= 1.3569357484949191d-134) then
        tmp = y0 * (x * -(j * b))
    else if (y5 <= 6.127283204794414d+81) then
        tmp = y2 * (k * (y1 * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y0 * (y3 * y5));
	double tmp;
	if (y5 <= -1.5800475277928215e+189) {
		tmp = k * ((i * y) * y5);
	} else if (y5 <= -2.82939017794136e+50) {
		tmp = t_1;
	} else if (y5 <= 4.115958861025253e-262) {
		tmp = (-(y2 * c) * y4) * t;
	} else if (y5 <= 1.3569357484949191e-134) {
		tmp = y0 * (x * -(j * b));
	} else if (y5 <= 6.127283204794414e+81) {
		tmp = y2 * (k * (y1 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y0 * (y3 * y5))
	tmp = 0
	if y5 <= -1.5800475277928215e+189:
		tmp = k * ((i * y) * y5)
	elif y5 <= -2.82939017794136e+50:
		tmp = t_1
	elif y5 <= 4.115958861025253e-262:
		tmp = (-(y2 * c) * y4) * t
	elif y5 <= 1.3569357484949191e-134:
		tmp = y0 * (x * -(j * b))
	elif y5 <= 6.127283204794414e+81:
		tmp = y2 * (k * (y1 * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y0 * Float64(y3 * y5)))
	tmp = 0.0
	if (y5 <= -1.5800475277928215e+189)
		tmp = Float64(k * Float64(Float64(i * y) * y5));
	elseif (y5 <= -2.82939017794136e+50)
		tmp = t_1;
	elseif (y5 <= 4.115958861025253e-262)
		tmp = Float64(Float64(Float64(-Float64(y2 * c)) * y4) * t);
	elseif (y5 <= 1.3569357484949191e-134)
		tmp = Float64(y0 * Float64(x * Float64(-Float64(j * b))));
	elseif (y5 <= 6.127283204794414e+81)
		tmp = Float64(y2 * Float64(k * Float64(y1 * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (y0 * (y3 * y5));
	tmp = 0.0;
	if (y5 <= -1.5800475277928215e+189)
		tmp = k * ((i * y) * y5);
	elseif (y5 <= -2.82939017794136e+50)
		tmp = t_1;
	elseif (y5 <= 4.115958861025253e-262)
		tmp = (-(y2 * c) * y4) * t;
	elseif (y5 <= 1.3569357484949191e-134)
		tmp = y0 * (x * -(j * b));
	elseif (y5 <= 6.127283204794414e+81)
		tmp = y2 * (k * (y1 * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.5800475277928215e+189], N[(k * N[(N[(i * y), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.82939017794136e+50], t$95$1, If[LessEqual[y5, 4.115958861025253e-262], N[(N[((-N[(y2 * c), $MachinePrecision]) * y4), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y5, 1.3569357484949191e-134], N[(y0 * N[(x * (-N[(j * b), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6.127283204794414e+81], N[(y2 * N[(k * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (j * (y0 * (y3 * y5))) IN
		LET tmp_4 = IF (y5 <= (6127283204794413890581259870022779023214617512132069659033505421795611026231656448)) THEN (y2 * (k * (y1 * y4))) ELSE t_1 ENDIF IN
		LET tmp_3 = IF (y5 <= (1356935748494919128011054354439352447934477536854172157834796498856968184672510314422642111558158232402707950641458694379370897548128151148372369363680578207458745151760917302489666863399938185565526722809794982167796433862225984420149852805083122527031643113759730033777605942962929622674957149244929429135290691857659351772513733891400988795794546604156494140625e-497)) THEN (y0 * (x * (- (j * b)))) ELSE tmp_4 ENDIF IN
		LET tmp_2 = IF (y5 <= (411595886102525315527544067255172433395255551520555174083963067758041230957240192923662982557049797958310462433153471930102487076228868321298856831566499550055032768383095072369565238300768195551716169080393893716463887557961923980677819770960936212365490148435715055564384576309545517064233202098119410419469811509805117410725859477136027920294286942585824120154119214152102471100788534791551271869831990556512141934883159014899382086334944871651372485216513338657300184362588314391314864424054671789659608908963498399024022623809444076525373933693696358014746187733364672528405299368137141396536947268748568001993045663289283453423195169307291507720947265625e-921)) THEN (((- (y2 * c)) * y4) * t) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (y5 <= (-282939017794136019768778887573958489561264807739392)) THEN t_1 ELSE tmp_2 ENDIF IN
		LET tmp = IF (y5 <= (-1580047527792821508643324012569263285441376655464830329581682644176629442742749411117031682488271577633271751776168801701621061354015935631401221876714727786113253247273803210073196961202176)) THEN (k * ((i * y) * y5)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if y5 < -1.5800475277928215e189

   1. Initial program 29.3%

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

   2. Taylor expanded in k around inf

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

   4. Applied rewrites 36.7%

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

   5. Taylor expanded in i around inf

      \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.5%

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

   8. Taylor expanded in y around inf

      \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.6%

       \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 17.6%

       \[\leadsto k \cdot \left(\left(i \cdot y\right) \cdot y5\right) \]

   if -1.5800475277928215e189 < y5 < -2.8293901779413602e50 or 6.1272832047944139e81 < y5

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in y0 around inf

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

   7. Applied rewrites 26.8%

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

   8. Taylor expanded in x around 0

      \[\leadsto j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.8%

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

   if -2.8293901779413602e50 < y5 < 4.1159588610252532e-262

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

      \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) \]

   8. Taylor expanded in b around 0

      \[\leadsto t \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot y2\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.0%

       \[\leadsto t \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot y2\right)\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 17.0%

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

   if 4.1159588610252532e-262 < y5 < 1.3569357484949191e-134

   1. Initial program 29.3%

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

   2. Taylor expanded in y0 around inf

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

   4. Applied rewrites 36.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.4%

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

   8. Taylor expanded in b around inf

      \[\leadsto y0 \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot j\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.0%

       \[\leadsto y0 \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot j\right)\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 17.0%

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

   if 1.3569357484949191e-134 < y5 < 6.1272832047944139e81

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

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

   8. Taylor expanded in y4 around inf

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.0%

       \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 34: 22.6% accurate, 4.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y2 \leq -1.8794579877061817 \cdot 10^{+77}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -6.698783381092405 \cdot 10^{-21}:\\ \;\;\;\;\left(-\left(y2 \cdot x\right) \cdot a\right) \cdot y1\\ \mathbf{elif}\;y2 \leq -1.0157945730164344 \cdot 10^{-188}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -6.326770153524444 \cdot 10^{-295}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 5.288765309617244 \cdot 10^{-81}:\\ \;\;\;\;-\left(\left(y1 \cdot j\right) \cdot y4\right) \cdot y3\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= y2 -1.8794579877061817e+77)
  (* a (* t (* y2 y5)))
  (if (<= y2 -6.698783381092405e-21)
    (* (- (* (* y2 x) a)) y1)
    (if (<= y2 -1.0157945730164344e-188)
      (* j (* b (* t y4)))
      (if (<= y2 -6.326770153524444e-295)
        (* y0 (* y3 (* j y5)))
        (if (<= y2 5.288765309617244e-81)
          (- (* (* (* y1 j) y4) y3))
          (* k (* y4 (* y1 y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.8794579877061817e+77) {
		tmp = a * (t * (y2 * y5));
	} else if (y2 <= -6.698783381092405e-21) {
		tmp = -((y2 * x) * a) * y1;
	} else if (y2 <= -1.0157945730164344e-188) {
		tmp = j * (b * (t * y4));
	} else if (y2 <= -6.326770153524444e-295) {
		tmp = y0 * (y3 * (j * y5));
	} else if (y2 <= 5.288765309617244e-81) {
		tmp = -(((y1 * j) * y4) * y3);
	} else {
		tmp = k * (y4 * (y1 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.8794579877061817d+77)) then
        tmp = a * (t * (y2 * y5))
    else if (y2 <= (-6.698783381092405d-21)) then
        tmp = -((y2 * x) * a) * y1
    else if (y2 <= (-1.0157945730164344d-188)) then
        tmp = j * (b * (t * y4))
    else if (y2 <= (-6.326770153524444d-295)) then
        tmp = y0 * (y3 * (j * y5))
    else if (y2 <= 5.288765309617244d-81) then
        tmp = -(((y1 * j) * y4) * y3)
    else
        tmp = k * (y4 * (y1 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.8794579877061817e+77) {
		tmp = a * (t * (y2 * y5));
	} else if (y2 <= -6.698783381092405e-21) {
		tmp = -((y2 * x) * a) * y1;
	} else if (y2 <= -1.0157945730164344e-188) {
		tmp = j * (b * (t * y4));
	} else if (y2 <= -6.326770153524444e-295) {
		tmp = y0 * (y3 * (j * y5));
	} else if (y2 <= 5.288765309617244e-81) {
		tmp = -(((y1 * j) * y4) * y3);
	} else {
		tmp = k * (y4 * (y1 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.8794579877061817e+77:
		tmp = a * (t * (y2 * y5))
	elif y2 <= -6.698783381092405e-21:
		tmp = -((y2 * x) * a) * y1
	elif y2 <= -1.0157945730164344e-188:
		tmp = j * (b * (t * y4))
	elif y2 <= -6.326770153524444e-295:
		tmp = y0 * (y3 * (j * y5))
	elif y2 <= 5.288765309617244e-81:
		tmp = -(((y1 * j) * y4) * y3)
	else:
		tmp = k * (y4 * (y1 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.8794579877061817e+77)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (y2 <= -6.698783381092405e-21)
		tmp = Float64(Float64(-Float64(Float64(y2 * x) * a)) * y1);
	elseif (y2 <= -1.0157945730164344e-188)
		tmp = Float64(j * Float64(b * Float64(t * y4)));
	elseif (y2 <= -6.326770153524444e-295)
		tmp = Float64(y0 * Float64(y3 * Float64(j * y5)));
	elseif (y2 <= 5.288765309617244e-81)
		tmp = Float64(-Float64(Float64(Float64(y1 * j) * y4) * y3));
	else
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.8794579877061817e+77)
		tmp = a * (t * (y2 * y5));
	elseif (y2 <= -6.698783381092405e-21)
		tmp = -((y2 * x) * a) * y1;
	elseif (y2 <= -1.0157945730164344e-188)
		tmp = j * (b * (t * y4));
	elseif (y2 <= -6.326770153524444e-295)
		tmp = y0 * (y3 * (j * y5));
	elseif (y2 <= 5.288765309617244e-81)
		tmp = -(((y1 * j) * y4) * y3);
	else
		tmp = k * (y4 * (y1 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.8794579877061817e+77], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6.698783381092405e-21], N[((-N[(N[(y2 * x), $MachinePrecision] * a), $MachinePrecision]) * y1), $MachinePrecision], If[LessEqual[y2, -1.0157945730164344e-188], N[(j * N[(b * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6.326770153524444e-295], N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.288765309617244e-81], (-N[(N[(N[(y1 * j), $MachinePrecision] * y4), $MachinePrecision] * y3), $MachinePrecision]), N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_4 = IF (y2 <= (52887653096172443307702244731092265514934934702031508617739331335333646279900423650613010029708645487368011902360816955324012178279738907647264661082064385579714912190817380545763763838557652732612346380136614243383519351482391357421875e-316)) THEN (- (((y1 * j) * y4) * y3)) ELSE (k * (y4 * (y1 * y2))) ENDIF IN
	LET tmp_3 = IF (y2 <= (-63267701535244441791748498479104258374644319547557499521150432805483267476048389247630991015275993732740914949231235174690105522898293443994013958194877949309020257888419931798373769187092460107897269795781813135046529204049069102332682000316328081467990252902977075180488700041851343425282953643020475812433333858818383717678151203439661902704137765313029080181572066848998364102082548545727036422853994233659481541906851072938292484794070466906923365050313206952271034520721820383096341278949761697259056966748080390575490331196223390516895363809975011098578910932028261104975492219672842947093790512619328178100990065019125746829094450925249489262178211029683364369024841599257423838432458883251907622025100863538682460784912109375e-1028)) THEN (y0 * (y3 * (j * y5))) ELSE tmp_4 ENDIF IN
	LET tmp_2 = IF (y2 <= (-1015794573016434400166387276039280414351996542209707084996214688334350980400867486451262956438387586484509915667151393468104668122796893500980576029791418054376822631826347722288908528796733245908771469785211762197005955443483690458773801798640962731841635173656087908855887096983436562903071138275074742952049559338597594116725677683269240042002427570424495883293148771711424517451434622409149807946392517225289062059838993514907617051871495814844952032540703612539800815284252166748046875e-677)) THEN (j * (b * (t * y4))) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (y2 <= (-6698783381092405140802303664398764919425305382151810741110653513175066109397448599338531494140625e-117)) THEN ((- ((y2 * x) * a)) * y1) ELSE tmp_2 ENDIF IN
	LET tmp = IF (y2 <= (-187945798770618167324822901327878523740849739723978445185383430409301748875264)) THEN (a * (t * (y2 * y5))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 6 regimes

2. if y2 < -1.8794579877061817e77

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.6%

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

   if -1.8794579877061817e77 < y2 < -6.6987833810924051e-21

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   5. Taylor expanded in y1 around inf

      \[\leadsto y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y1 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, a \cdot x, k \cdot y4\right)\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.4%

       \[\leadsto y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)\right) \]

   12. Applied rewrites 17.4%

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

   if -6.6987833810924051e-21 < y2 < -1.0157945730164344e-188

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.0%

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

   8. Taylor expanded in x around 0

      \[\leadsto j \cdot \left(b \cdot \left(t \cdot y4\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.3%

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

   if -1.0157945730164344e-188 < y2 < -6.3267701535244442e-295

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.8%

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

   if -6.3267701535244442e-295 < y2 < 5.2887653096172443e-81

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y4 around inf

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

   7. Applied rewrites 26.6%

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

   8. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \left(y3 \cdot \left(y4 \cdot \left(j \cdot y1\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.9%

       \[\leadsto -1 \cdot \left(y3 \cdot \left(y4 \cdot \left(j \cdot y1\right)\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 16.9%

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

   if 5.2887653096172443e-81 < y2

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in k around inf

      \[\leadsto k \cdot \left(y4 \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.8%

      \[\leadsto k \cdot \left(y4 \cdot \mathsf{fma}\left(-1, b \cdot y, y1 \cdot y2\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.9%

       \[\leadsto k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 35: 22.1% accurate, 5.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y3 \leq -7.168982209588523 \cdot 10^{-43}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -6.639275725559344 \cdot 10^{-292}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq 1.2729087239749634 \cdot 10^{-8}:\\ \;\;\;\;\left(-\left(y2 \cdot x\right) \cdot a\right) \cdot y1\\ \mathbf{elif}\;y3 \leq 3.5472742916873207 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= y3 -7.168982209588523e-43)
  (* j (* y5 (* y0 y3)))
  (if (<= y3 -6.639275725559344e-292)
    (* k (* (* i y) y5))
    (if (<= y3 1.2729087239749634e-8)
      (* (- (* (* y2 x) a)) y1)
      (if (<= y3 3.5472742916873207e+105)
        (* a (* t (* y2 y5)))
        (* c (* y (* y3 y4))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -7.168982209588523e-43) {
		tmp = j * (y5 * (y0 * y3));
	} else if (y3 <= -6.639275725559344e-292) {
		tmp = k * ((i * y) * y5);
	} else if (y3 <= 1.2729087239749634e-8) {
		tmp = -((y2 * x) * a) * y1;
	} else if (y3 <= 3.5472742916873207e+105) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = c * (y * (y3 * y4));
	}
	return tmp;
}

Fortran

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 <= (-7.168982209588523d-43)) then
        tmp = j * (y5 * (y0 * y3))
    else if (y3 <= (-6.639275725559344d-292)) then
        tmp = k * ((i * y) * y5)
    else if (y3 <= 1.2729087239749634d-8) then
        tmp = -((y2 * x) * a) * y1
    else if (y3 <= 3.5472742916873207d+105) then
        tmp = a * (t * (y2 * y5))
    else
        tmp = c * (y * (y3 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -7.168982209588523e-43) {
		tmp = j * (y5 * (y0 * y3));
	} else if (y3 <= -6.639275725559344e-292) {
		tmp = k * ((i * y) * y5);
	} else if (y3 <= 1.2729087239749634e-8) {
		tmp = -((y2 * x) * a) * y1;
	} else if (y3 <= 3.5472742916873207e+105) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = c * (y * (y3 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -7.168982209588523e-43:
		tmp = j * (y5 * (y0 * y3))
	elif y3 <= -6.639275725559344e-292:
		tmp = k * ((i * y) * y5)
	elif y3 <= 1.2729087239749634e-8:
		tmp = -((y2 * x) * a) * y1
	elif y3 <= 3.5472742916873207e+105:
		tmp = a * (t * (y2 * y5))
	else:
		tmp = c * (y * (y3 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -7.168982209588523e-43)
		tmp = Float64(j * Float64(y5 * Float64(y0 * y3)));
	elseif (y3 <= -6.639275725559344e-292)
		tmp = Float64(k * Float64(Float64(i * y) * y5));
	elseif (y3 <= 1.2729087239749634e-8)
		tmp = Float64(Float64(-Float64(Float64(y2 * x) * a)) * y1);
	elseif (y3 <= 3.5472742916873207e+105)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -7.168982209588523e-43)
		tmp = j * (y5 * (y0 * y3));
	elseif (y3 <= -6.639275725559344e-292)
		tmp = k * ((i * y) * y5);
	elseif (y3 <= 1.2729087239749634e-8)
		tmp = -((y2 * x) * a) * y1;
	elseif (y3 <= 3.5472742916873207e+105)
		tmp = a * (t * (y2 * y5));
	else
		tmp = c * (y * (y3 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -7.168982209588523e-43], N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -6.639275725559344e-292], N[(k * N[(N[(i * y), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.2729087239749634e-8], N[((-N[(N[(y2 * x), $MachinePrecision] * a), $MachinePrecision]) * y1), $MachinePrecision], If[LessEqual[y3, 3.5472742916873207e+105], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_3 = IF (y3 <= (3547274291687320675661792083569982051295070801757212167169974379171327579334679228065967075306414450671616)) THEN (a * (t * (y2 * y5))) ELSE (c * (y * (y3 * y4))) ENDIF IN
	LET tmp_2 = IF (y3 <= (12729087239749633980701479739859605100349426720640622079372406005859375e-78)) THEN ((- ((y2 * x) * a)) * y1) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (y3 <= (-66392757255593441711666195855790007518233384221532879701374594836417291258458931450293501421041161013989579122699724975860955355171299822118081121190494185411398030626663858100282409350847960925569755455125803036019227390970461499907772278369255612926685369039266844196865547593787780888581030795960805026970661330869008691903699406237674213940060607397605643065882271901248450638654799401183709470763865353358887750104052928978510614821911430247687593452857402484049471110453030940840311839845093627897235982383532589134541562450888647112655765693867487522243133453610593672146462573065656652044195112345097842267114145659805952892082453344247543383186526823842547735536602525731756708517183884765699986019171774387359619140625e-1019)) THEN (k * ((i * y) * y5)) ELSE tmp_2 ENDIF IN
	LET tmp = IF (y3 <= (-7168982209588523179045006259587997209734532348920603774587925436597347207098633354357162253693684703562236278095998187609438900835812091827392578125e-190)) THEN (j * (y5 * (y0 * y3))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 5 regimes

2. if y3 < -7.1689822095885232e-43

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in j around -inf

      \[\leadsto j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.5%

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

   8. Taylor expanded in t around 0

      \[\leadsto j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.9%

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

   if -7.1689822095885232e-43 < y3 < -6.6392757255593442e-292

   1. Initial program 29.3%

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

   2. Taylor expanded in k around inf

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

   4. Applied rewrites 36.7%

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

   5. Taylor expanded in i around inf

      \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.5%

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

   8. Taylor expanded in y around inf

      \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.6%

       \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 17.6%

       \[\leadsto k \cdot \left(\left(i \cdot y\right) \cdot y5\right) \]

   if -6.6392757255593442e-292 < y3 < 1.2729087239749634e-8

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   5. Taylor expanded in y1 around inf

      \[\leadsto y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.7%

      \[\leadsto y1 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, a \cdot x, k \cdot y4\right)\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.4%

       \[\leadsto y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)\right) \]

   12. Applied rewrites 17.4%

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

   if 1.2729087239749634e-8 < y3 < 3.5472742916873207e105

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.6%

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

   if 3.5472742916873207e105 < y3

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in c around inf

      \[\leadsto c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.4%

       \[\leadsto c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 36: 22.0% accurate, 6.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y1 \leq -1.6805478782108169 \cdot 10^{+218}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -2.5936942577544745 \cdot 10^{+42}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 5.955798557871136 \cdot 10^{+64}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= y1 -1.6805478782108169e+218)
  (* j (* x (* i y1)))
  (if (<= y1 -2.5936942577544745e+42)
    (* k (* y4 (* y1 y2)))
    (if (<= y1 5.955798557871136e+64)
      (* y0 (* y3 (* j y5)))
      (* y2 (* k (* y1 y4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -1.6805478782108169e+218) {
		tmp = j * (x * (i * y1));
	} else if (y1 <= -2.5936942577544745e+42) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y1 <= 5.955798557871136e+64) {
		tmp = y0 * (y3 * (j * y5));
	} else {
		tmp = y2 * (k * (y1 * y4));
	}
	return tmp;
}

Fortran

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 <= (-1.6805478782108169d+218)) then
        tmp = j * (x * (i * y1))
    else if (y1 <= (-2.5936942577544745d+42)) then
        tmp = k * (y4 * (y1 * y2))
    else if (y1 <= 5.955798557871136d+64) then
        tmp = y0 * (y3 * (j * y5))
    else
        tmp = y2 * (k * (y1 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -1.6805478782108169e+218) {
		tmp = j * (x * (i * y1));
	} else if (y1 <= -2.5936942577544745e+42) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y1 <= 5.955798557871136e+64) {
		tmp = y0 * (y3 * (j * y5));
	} else {
		tmp = y2 * (k * (y1 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -1.6805478782108169e+218:
		tmp = j * (x * (i * y1))
	elif y1 <= -2.5936942577544745e+42:
		tmp = k * (y4 * (y1 * y2))
	elif y1 <= 5.955798557871136e+64:
		tmp = y0 * (y3 * (j * y5))
	else:
		tmp = y2 * (k * (y1 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -1.6805478782108169e+218)
		tmp = Float64(j * Float64(x * Float64(i * y1)));
	elseif (y1 <= -2.5936942577544745e+42)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (y1 <= 5.955798557871136e+64)
		tmp = Float64(y0 * Float64(y3 * Float64(j * y5)));
	else
		tmp = Float64(y2 * Float64(k * Float64(y1 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -1.6805478782108169e+218)
		tmp = j * (x * (i * y1));
	elseif (y1 <= -2.5936942577544745e+42)
		tmp = k * (y4 * (y1 * y2));
	elseif (y1 <= 5.955798557871136e+64)
		tmp = y0 * (y3 * (j * y5));
	else
		tmp = y2 * (k * (y1 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -1.6805478782108169e+218], N[(j * N[(x * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.5936942577544745e+42], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.955798557871136e+64], N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(k * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_2 = IF (y1 <= (59557985578711355417717242254308632781943095888219829808937304064)) THEN (y0 * (y3 * (j * y5))) ELSE (y2 * (k * (y1 * y4))) ENDIF IN
	LET tmp_1 = IF (y1 <= (-2593694257754474544317195334463245101563904)) THEN (k * (y4 * (y1 * y2))) ELSE tmp_2 ENDIF IN
	LET tmp = IF (y1 <= (-168054787821081689501612617277845314116980330694614899400476176546908608340173426751821996065552536810597405038234402975400849771337226106583984700609589830641482086114097073631014315778513773240906921680571546325745664)) THEN (j * (x * (i * y1))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if y1 < -1.6805478782108169e218

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 27.5%

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

   8. Taylor expanded in b around 0

      \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.3%

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

   if -1.6805478782108169e218 < y1 < -2.5936942577544745e42

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in k around inf

      \[\leadsto k \cdot \left(y4 \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.8%

      \[\leadsto k \cdot \left(y4 \cdot \mathsf{fma}\left(-1, b \cdot y, y1 \cdot y2\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.9%

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

   if -2.5936942577544745e42 < y1 < 5.9557985578711355e64

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.8%

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

   if 5.9557985578711355e64 < y1

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

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

   8. Taylor expanded in y4 around inf

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.0%

       \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 37: 22.0% accurate, 6.3× speedup

Math

\[\begin{array}{l} t_1 := y2 \cdot \left(k \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{if}\;y1 \leq -9.926725124927276 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -4.293007455925721 \cdot 10^{-38}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 5.955798557871136 \cdot 10^{+64}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* y2 (* k (* y1 y4)))))
  (if (<= y1 -9.926725124927276e+117)
    t_1
    (if (<= y1 -4.293007455925721e-38)
      (* b (* j (* t y4)))
      (if (<= y1 5.955798557871136e+64) (* y0 (* y3 (* j y5))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (k * (y1 * y4));
	double tmp;
	if (y1 <= -9.926725124927276e+117) {
		tmp = t_1;
	} else if (y1 <= -4.293007455925721e-38) {
		tmp = b * (j * (t * y4));
	} else if (y1 <= 5.955798557871136e+64) {
		tmp = y0 * (y3 * (j * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = y2 * (k * (y1 * y4))
    if (y1 <= (-9.926725124927276d+117)) then
        tmp = t_1
    else if (y1 <= (-4.293007455925721d-38)) then
        tmp = b * (j * (t * y4))
    else if (y1 <= 5.955798557871136d+64) then
        tmp = y0 * (y3 * (j * y5))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (k * (y1 * y4));
	double tmp;
	if (y1 <= -9.926725124927276e+117) {
		tmp = t_1;
	} else if (y1 <= -4.293007455925721e-38) {
		tmp = b * (j * (t * y4));
	} else if (y1 <= 5.955798557871136e+64) {
		tmp = y0 * (y3 * (j * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (k * (y1 * y4))
	tmp = 0
	if y1 <= -9.926725124927276e+117:
		tmp = t_1
	elif y1 <= -4.293007455925721e-38:
		tmp = b * (j * (t * y4))
	elif y1 <= 5.955798557871136e+64:
		tmp = y0 * (y3 * (j * y5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(k * Float64(y1 * y4)))
	tmp = 0.0
	if (y1 <= -9.926725124927276e+117)
		tmp = t_1;
	elseif (y1 <= -4.293007455925721e-38)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (y1 <= 5.955798557871136e+64)
		tmp = Float64(y0 * Float64(y3 * Float64(j * y5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (k * (y1 * y4));
	tmp = 0.0;
	if (y1 <= -9.926725124927276e+117)
		tmp = t_1;
	elseif (y1 <= -4.293007455925721e-38)
		tmp = b * (j * (t * y4));
	elseif (y1 <= 5.955798557871136e+64)
		tmp = y0 * (y3 * (j * y5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(k * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -9.926725124927276e+117], t$95$1, If[LessEqual[y1, -4.293007455925721e-38], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.955798557871136e+64], N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (y2 * (k * (y1 * y4))) IN
		LET tmp_2 = IF (y1 <= (59557985578711355417717242254308632781943095888219829808937304064)) THEN (y0 * (y3 * (j * y5))) ELSE t_1 ENDIF IN
		LET tmp_1 = IF (y1 <= (-42930074559257211770186329533068826449928936804310201351053396401036553413607569632185273043138424957365639755835218238644301891326904296875e-177)) THEN (b * (j * (t * y4))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (y1 <= (-9926725124927275844200613311280745769550040482931729866525962942985132719712544916869387199414605928310406626414690304)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if y1 < -9.9267251249272758e117 or 5.9557985578711355e64 < y1

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

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

   8. Taylor expanded in y4 around inf

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.0%

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

   if -9.9267251249272758e117 < y1 < -4.2930074559257212e-38

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

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

   8. Taylor expanded in x around 0

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.3%

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

   if -4.2930074559257212e-38 < y1 < 5.9557985578711355e64

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.8%

       \[\leadsto y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 38: 21.8% accurate, 6.3× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{if}\;y0 \leq -1.3245391277762227 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 6.5275979808792474 \cdot 10^{-217}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.0984970379621386 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* j (* y5 (* y0 y3)))))
  (if (<= y0 -1.3245391277762227e+135)
    t_1
    (if (<= y0 6.5275979808792474e-217)
      (* a (* y5 (* t y2)))
      (if (<= y0 1.0984970379621386e-56) (* b (* j (* t y4))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y5 * (y0 * y3));
	double tmp;
	if (y0 <= -1.3245391277762227e+135) {
		tmp = t_1;
	} else if (y0 <= 6.5275979808792474e-217) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 1.0984970379621386e-56) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (y5 * (y0 * y3))
    if (y0 <= (-1.3245391277762227d+135)) then
        tmp = t_1
    else if (y0 <= 6.5275979808792474d-217) then
        tmp = a * (y5 * (t * y2))
    else if (y0 <= 1.0984970379621386d-56) then
        tmp = b * (j * (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y5 * (y0 * y3));
	double tmp;
	if (y0 <= -1.3245391277762227e+135) {
		tmp = t_1;
	} else if (y0 <= 6.5275979808792474e-217) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 1.0984970379621386e-56) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y5 * (y0 * y3))
	tmp = 0
	if y0 <= -1.3245391277762227e+135:
		tmp = t_1
	elif y0 <= 6.5275979808792474e-217:
		tmp = a * (y5 * (t * y2))
	elif y0 <= 1.0984970379621386e-56:
		tmp = b * (j * (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y5 * Float64(y0 * y3)))
	tmp = 0.0
	if (y0 <= -1.3245391277762227e+135)
		tmp = t_1;
	elseif (y0 <= 6.5275979808792474e-217)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y0 <= 1.0984970379621386e-56)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (y5 * (y0 * y3));
	tmp = 0.0;
	if (y0 <= -1.3245391277762227e+135)
		tmp = t_1;
	elseif (y0 <= 6.5275979808792474e-217)
		tmp = a * (y5 * (t * y2));
	elseif (y0 <= 1.0984970379621386e-56)
		tmp = b * (j * (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.3245391277762227e+135], t$95$1, If[LessEqual[y0, 6.5275979808792474e-217], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.0984970379621386e-56], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (j * (y5 * (y0 * y3))) IN
		LET tmp_2 = IF (y0 <= (109849703796213859489799205710342641350592242587499477779020829357300667729217435864119657480462466131123418333256807320993293486367983673797528443305537848573294468224048614501953125e-238)) THEN (b * (j * (t * y4))) ELSE t_1 ENDIF IN
		LET tmp_1 = IF (y0 <= (652759798087924743622837789884514224813283620131888232265421373878884879936425219877319113692409409965486587530557974033028662850899470921307392163269855645821307789378324552000074604272125659997232775860280583263231284730467795649304137499304783942601784314572638340941204443871792219567832698654207228334213737736498880696477257384136531770434170110795813795155247342952609959182779688947751986551702339029586912002966957862254429007768477528790099313359876314702526823581625677924686587709118520491555864206502206303905921913610654883086681365966796875e-771)) THEN (a * (y5 * (t * y2))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (y0 <= (-1324539127776222702900886589461002021849043491402616329115005573967141549173928882254980638685702321446431495723991033565032559771910144)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if y0 < -1.3245391277762227e135 or 1.0984970379621386e-56 < y0

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in j around -inf

      \[\leadsto j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.5%

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

   8. Taylor expanded in t around 0

      \[\leadsto j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.9%

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

   if -1.3245391277762227e135 < y0 < 6.5275979808792474e-217

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.4%

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

   if 6.5275979808792474e-217 < y0 < 1.0984970379621386e-56

   1. Initial program 29.3%

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

   2. Taylor expanded in j around inf

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

   4. Applied rewrites 35.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

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

   8. Taylor expanded in x around 0

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.3%

       \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 39: 21.5% accurate, 7.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y1 \leq -2.5936942577544745 \cdot 10^{+42}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 5.955798557871136 \cdot 10^{+64}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (if (<= y1 -2.5936942577544745e+42)
  (* k (* y4 (* y1 y2)))
  (if (<= y1 5.955798557871136e+64)
    (* y0 (* y3 (* j y5)))
    (* y2 (* k (* y1 y4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -2.5936942577544745e+42) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y1 <= 5.955798557871136e+64) {
		tmp = y0 * (y3 * (j * y5));
	} else {
		tmp = y2 * (k * (y1 * y4));
	}
	return tmp;
}

Fortran

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 <= (-2.5936942577544745d+42)) then
        tmp = k * (y4 * (y1 * y2))
    else if (y1 <= 5.955798557871136d+64) then
        tmp = y0 * (y3 * (j * y5))
    else
        tmp = y2 * (k * (y1 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -2.5936942577544745e+42) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y1 <= 5.955798557871136e+64) {
		tmp = y0 * (y3 * (j * y5));
	} else {
		tmp = y2 * (k * (y1 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -2.5936942577544745e+42:
		tmp = k * (y4 * (y1 * y2))
	elif y1 <= 5.955798557871136e+64:
		tmp = y0 * (y3 * (j * y5))
	else:
		tmp = y2 * (k * (y1 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -2.5936942577544745e+42)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (y1 <= 5.955798557871136e+64)
		tmp = Float64(y0 * Float64(y3 * Float64(j * y5)));
	else
		tmp = Float64(y2 * Float64(k * Float64(y1 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -2.5936942577544745e+42)
		tmp = k * (y4 * (y1 * y2));
	elseif (y1 <= 5.955798557871136e+64)
		tmp = y0 * (y3 * (j * y5));
	else
		tmp = y2 * (k * (y1 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -2.5936942577544745e+42], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.955798557871136e+64], N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(k * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET tmp_1 = IF (y1 <= (59557985578711355417717242254308632781943095888219829808937304064)) THEN (y0 * (y3 * (j * y5))) ELSE (y2 * (k * (y1 * y4))) ENDIF IN
	LET tmp = IF (y1 <= (-2593694257754474544317195334463245101563904)) THEN (k * (y4 * (y1 * y2))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if y1 < -2.5936942577544745e42

   1. Initial program 29.3%

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

   2. Taylor expanded in y4 around inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in k around inf

      \[\leadsto k \cdot \left(y4 \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.8%

      \[\leadsto k \cdot \left(y4 \cdot \mathsf{fma}\left(-1, b \cdot y, y1 \cdot y2\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.9%

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

   if -2.5936942577544745e42 < y1 < 5.9557985578711355e64

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.8%

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

   if 5.9557985578711355e64 < y1

   1. Initial program 29.3%

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

   2. Taylor expanded in y2 around inf

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

   4. Applied rewrites 37.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

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

   8. Taylor expanded in y4 around inf

      \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.0%

       \[\leadsto y2 \cdot \left(k \cdot \left(y1 \cdot y4\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 40: 21.2% accurate, 6.3× speedup

Math

\[\begin{array}{l} t_1 := y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;j \leq -2.0763357087301076 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5.734249425475759 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 2.5949901733941258 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* y0 (* y3 (* j y5)))))
  (if (<= j -2.0763357087301076e+48)
    t_1
    (if (<= j -5.734249425475759e-143)
      (* a (* y5 (* t y2)))
      (if (<= j 2.5949901733941258e-40) (* a (* y1 (* y3 z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y3 * (j * y5));
	double tmp;
	if (j <= -2.0763357087301076e+48) {
		tmp = t_1;
	} else if (j <= -5.734249425475759e-143) {
		tmp = a * (y5 * (t * y2));
	} else if (j <= 2.5949901733941258e-40) {
		tmp = a * (y1 * (y3 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = y0 * (y3 * (j * y5))
    if (j <= (-2.0763357087301076d+48)) then
        tmp = t_1
    else if (j <= (-5.734249425475759d-143)) then
        tmp = a * (y5 * (t * y2))
    else if (j <= 2.5949901733941258d-40) then
        tmp = a * (y1 * (y3 * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y3 * (j * y5));
	double tmp;
	if (j <= -2.0763357087301076e+48) {
		tmp = t_1;
	} else if (j <= -5.734249425475759e-143) {
		tmp = a * (y5 * (t * y2));
	} else if (j <= 2.5949901733941258e-40) {
		tmp = a * (y1 * (y3 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y3 * (j * y5))
	tmp = 0
	if j <= -2.0763357087301076e+48:
		tmp = t_1
	elif j <= -5.734249425475759e-143:
		tmp = a * (y5 * (t * y2))
	elif j <= 2.5949901733941258e-40:
		tmp = a * (y1 * (y3 * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(y3 * Float64(j * y5)))
	tmp = 0.0
	if (j <= -2.0763357087301076e+48)
		tmp = t_1;
	elseif (j <= -5.734249425475759e-143)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (j <= 2.5949901733941258e-40)
		tmp = Float64(a * Float64(y1 * Float64(y3 * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (y3 * (j * y5));
	tmp = 0.0;
	if (j <= -2.0763357087301076e+48)
		tmp = t_1;
	elseif (j <= -5.734249425475759e-143)
		tmp = a * (y5 * (t * y2));
	elseif (j <= 2.5949901733941258e-40)
		tmp = a * (y1 * (y3 * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.0763357087301076e+48], t$95$1, If[LessEqual[j, -5.734249425475759e-143], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5949901733941258e-40], N[(a * N[(y1 * N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (y0 * (y3 * (j * y5))) IN
		LET tmp_2 = IF (j <= (25949901733941257808219340263891971374059602335498077284898590957919075850266633269700487889112723040828389908796225427067838609218597412109375e-182)) THEN (a * (y1 * (y3 * z))) ELSE t_1 ENDIF IN
		LET tmp_1 = IF (j <= (-57342494254757586790844295259221227310401290188075020884602464466593455445014232098027853074450335359688777110319229771941506547371500278287446773457152083067936351360922851753424985036608596449446445407555544490778766573603050097961016438216637120381172781619444884697355101682361429443034935813847132616496543015150342888175269010907981527026822110570947188534773886203765869140625e-525)) THEN (a * (y5 * (t * y2))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (j <= (-2076335708730107628255095152464436157122565111808)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if j < -2.0763357087301076e48 or 2.5949901733941258e-40 < j

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.8%

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

   if -2.0763357087301076e48 < j < -5.7342494254757587e-143

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.4%

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

   if -5.7342494254757587e-143 < j < 2.5949901733941258e-40

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

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

   7. Applied rewrites 26.7%

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

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.1%

       \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 41: 21.2% accurate, 6.3× speedup

Math

\[\begin{array}{l} t_1 := y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;j \leq -2.498558311542852 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5.734249425475759 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 2.5949901733941258 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* y0 (* y3 (* j y5)))))
  (if (<= j -2.498558311542852e-14)
    t_1
    (if (<= j -5.734249425475759e-143)
      (* a (* t (* y2 y5)))
      (if (<= j 2.5949901733941258e-40) (* a (* y1 (* y3 z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y3 * (j * y5));
	double tmp;
	if (j <= -2.498558311542852e-14) {
		tmp = t_1;
	} else if (j <= -5.734249425475759e-143) {
		tmp = a * (t * (y2 * y5));
	} else if (j <= 2.5949901733941258e-40) {
		tmp = a * (y1 * (y3 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = y0 * (y3 * (j * y5))
    if (j <= (-2.498558311542852d-14)) then
        tmp = t_1
    else if (j <= (-5.734249425475759d-143)) then
        tmp = a * (t * (y2 * y5))
    else if (j <= 2.5949901733941258d-40) then
        tmp = a * (y1 * (y3 * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y3 * (j * y5));
	double tmp;
	if (j <= -2.498558311542852e-14) {
		tmp = t_1;
	} else if (j <= -5.734249425475759e-143) {
		tmp = a * (t * (y2 * y5));
	} else if (j <= 2.5949901733941258e-40) {
		tmp = a * (y1 * (y3 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y3 * (j * y5))
	tmp = 0
	if j <= -2.498558311542852e-14:
		tmp = t_1
	elif j <= -5.734249425475759e-143:
		tmp = a * (t * (y2 * y5))
	elif j <= 2.5949901733941258e-40:
		tmp = a * (y1 * (y3 * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(y3 * Float64(j * y5)))
	tmp = 0.0
	if (j <= -2.498558311542852e-14)
		tmp = t_1;
	elseif (j <= -5.734249425475759e-143)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (j <= 2.5949901733941258e-40)
		tmp = Float64(a * Float64(y1 * Float64(y3 * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (y3 * (j * y5));
	tmp = 0.0;
	if (j <= -2.498558311542852e-14)
		tmp = t_1;
	elseif (j <= -5.734249425475759e-143)
		tmp = a * (t * (y2 * y5));
	elseif (j <= 2.5949901733941258e-40)
		tmp = a * (y1 * (y3 * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.498558311542852e-14], t$95$1, If[LessEqual[j, -5.734249425475759e-143], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5949901733941258e-40], N[(a * N[(y1 * N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (y0 * (y3 * (j * y5))) IN
		LET tmp_2 = IF (j <= (25949901733941257808219340263891971374059602335498077284898590957919075850266633269700487889112723040828389908796225427067838609218597412109375e-182)) THEN (a * (y1 * (y3 * z))) ELSE t_1 ENDIF IN
		LET tmp_1 = IF (j <= (-57342494254757586790844295259221227310401290188075020884602464466593455445014232098027853074450335359688777110319229771941506547371500278287446773457152083067936351360922851753424985036608596449446445407555544490778766573603050097961016438216637120381172781619444884697355101682361429443034935813847132616496543015150342888175269010907981527026822110570947188534773886203765869140625e-525)) THEN (a * (t * (y2 * y5))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (j <= (-2498558311542851896218060089848304433003830203607886772942947573028504848480224609375e-98)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if j < -2.4985583115428519e-14 or 2.5949901733941258e-40 < j

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.8%

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

   if -2.4985583115428519e-14 < j < -5.7342494254757587e-143

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.6%

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

   if -5.7342494254757587e-143 < j < 2.5949901733941258e-40

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

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

   7. Applied rewrites 26.7%

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

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.1%

       \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 42: 21.0% accurate, 7.7× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{if}\;y0 \leq -3.0662303281307393 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 1.0396988991248782 \cdot 10^{+43}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* j (* y5 (* y0 y3)))))
  (if (<= y0 -3.0662303281307393e+133)
    t_1
    (if (<= y0 1.0396988991248782e+43) (* a (* t (* y2 y5))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y5 * (y0 * y3));
	double tmp;
	if (y0 <= -3.0662303281307393e+133) {
		tmp = t_1;
	} else if (y0 <= 1.0396988991248782e+43) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (y5 * (y0 * y3))
    if (y0 <= (-3.0662303281307393d+133)) then
        tmp = t_1
    else if (y0 <= 1.0396988991248782d+43) then
        tmp = a * (t * (y2 * y5))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y5 * (y0 * y3));
	double tmp;
	if (y0 <= -3.0662303281307393e+133) {
		tmp = t_1;
	} else if (y0 <= 1.0396988991248782e+43) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y5 * (y0 * y3))
	tmp = 0
	if y0 <= -3.0662303281307393e+133:
		tmp = t_1
	elif y0 <= 1.0396988991248782e+43:
		tmp = a * (t * (y2 * y5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y5 * Float64(y0 * y3)))
	tmp = 0.0
	if (y0 <= -3.0662303281307393e+133)
		tmp = t_1;
	elseif (y0 <= 1.0396988991248782e+43)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (y5 * (y0 * y3));
	tmp = 0.0;
	if (y0 <= -3.0662303281307393e+133)
		tmp = t_1;
	elseif (y0 <= 1.0396988991248782e+43)
		tmp = a * (t * (y2 * y5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3.0662303281307393e+133], t$95$1, If[LessEqual[y0, 1.0396988991248782e+43], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (j * (y5 * (y0 * y3))) IN
		LET tmp_1 = IF (y0 <= (10396988991248781552082670676265448522121216)) THEN (a * (t * (y2 * y5))) ELSE t_1 ENDIF IN
		LET tmp = IF (y0 <= (-30662303281307392619125158878972186807603461128812111743264439164155747648080940056024313081575927020327187307898589806878444790743040)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y0 < -3.0662303281307393e133 or 1.0396988991248782e43 < y0

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in j around -inf

      \[\leadsto j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.5%

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

   8. Taylor expanded in t around 0

      \[\leadsto j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.9%

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

   if -3.0662303281307393e133 < y0 < 1.0396988991248782e43

   1. Initial program 29.3%

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

   2. Taylor expanded in y5 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 26.0%

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.6%

       \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 43: 20.3% accurate, 7.7× speedup

Math

\[\begin{array}{l} t_1 := y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;j \leq -2.9775247863920854 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.5949901733941258 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* y0 (* y3 (* j y5)))))
  (if (<= j -2.9775247863920854e-158)
    t_1
    (if (<= j 2.5949901733941258e-40) (* a (* y1 (* y3 z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y3 * (j * y5));
	double tmp;
	if (j <= -2.9775247863920854e-158) {
		tmp = t_1;
	} else if (j <= 2.5949901733941258e-40) {
		tmp = a * (y1 * (y3 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = y0 * (y3 * (j * y5))
    if (j <= (-2.9775247863920854d-158)) then
        tmp = t_1
    else if (j <= 2.5949901733941258d-40) then
        tmp = a * (y1 * (y3 * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y3 * (j * y5));
	double tmp;
	if (j <= -2.9775247863920854e-158) {
		tmp = t_1;
	} else if (j <= 2.5949901733941258e-40) {
		tmp = a * (y1 * (y3 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y3 * (j * y5))
	tmp = 0
	if j <= -2.9775247863920854e-158:
		tmp = t_1
	elif j <= 2.5949901733941258e-40:
		tmp = a * (y1 * (y3 * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(y3 * Float64(j * y5)))
	tmp = 0.0
	if (j <= -2.9775247863920854e-158)
		tmp = t_1;
	elseif (j <= 2.5949901733941258e-40)
		tmp = Float64(a * Float64(y1 * Float64(y3 * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (y3 * (j * y5));
	tmp = 0.0;
	if (j <= -2.9775247863920854e-158)
		tmp = t_1;
	elseif (j <= 2.5949901733941258e-40)
		tmp = a * (y1 * (y3 * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.9775247863920854e-158], t$95$1, If[LessEqual[j, 2.5949901733941258e-40], N[(a * N[(y1 * N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	LET t_1 = (y0 * (y3 * (j * y5))) IN
		LET tmp_1 = IF (j <= (25949901733941257808219340263891971374059602335498077284898590957919075850266633269700487889112723040828389908796225427067838609218597412109375e-182)) THEN (a * (y1 * (y3 * z))) ELSE t_1 ENDIF IN
		LET tmp = IF (j <= (-29775247863920853922052839078900950329664692588254368557786851366383651203675310278685149312918409979888301438805055439713220177148225853053736753077070362571908569579373169440688522299928954407477549639511307269783642269159385843991528299748794019498752863649137225376179925413402651574558360501831126396740580437485909021577110648949908966353834362180313690077547779678696407944238355725019573583267629146575927734375e-576)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if j < -2.9775247863920854e-158 or 2.5949901733941258e-40 < j

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in y0 around -inf

      \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 25.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.8%

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

   if -2.9775247863920854e-158 < j < 2.5949901733941258e-40

   1. Initial program 29.3%

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

   2. Taylor expanded in y3 around -inf

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

   4. Applied rewrites 37.1%

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

   5. Taylor expanded in a around -inf

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

   7. Applied rewrites 26.7%

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

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 17.1%

       \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 44: 17.1% accurate, 13.5× speedup

Math

\[a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  :pre TRUE
  (* a (* y1 (* 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) {
	return a * (y1 * (y3 * z));
}

Fortran

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 * (y1 * (y3 * 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 * (y1 * (y3 * z));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y1 * N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf],
	i in [-inf, +inf],
	j in [-inf, +inf],
	k in [-inf, +inf],
	y0 in [-inf, +inf],
	y1 in [-inf, +inf],
	y2 in [-inf, +inf],
	y3 in [-inf, +inf],
	y4 in [-inf, +inf],
	y5 in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5: real): real =
	a * (y1 * (y3 * z))
END code

Derivation

1. Initial program 29.3%

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

2. Taylor expanded in y3 around -inf

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

4. Applied rewrites 37.1%

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

5. Taylor expanded in a around -inf

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

7. Applied rewrites 26.7%

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

8. Taylor expanded in y around 0

   \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]
9. Step-by-step derivation

10. Applied rewrites 17.1%

    \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(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)))))