Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 73.6% → 82.7%

Time: 28.6s

Alternatives: 24

Speedup: 0.5×

• 58.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
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) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
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) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(\frac{i \cdot b}{a} - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
          (* j (- (* c a) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* t (* a (- (/ (* i b) a) x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t * (a * (((i * b) / a) - x));
	}
	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 t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t * (a * (((i * b) / a) - x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = t * (a * (((i * b) / a) - x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(a * Float64(Float64(Float64(i * b) / a) - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = t * (a * (((i * b) / a) - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(a * N[(N[(N[(i * b), $MachinePrecision] / a), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 91.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 50.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z - a \cdot t\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;x \leq -1.04 \cdot 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-93}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-211}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-284}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{-302}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+15}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b))))
        (t_2 (* x (- (* y z) (* a t))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= x -1.04e+52)
     t_2
     (if (<= x -1.45e-93)
       (* y (- (* x z) (* j i)))
       (if (<= x -1.22e-143)
         (* a (- (* j c) (* x t)))
         (if (<= x -1.35e-211)
           (* b (- (* t i) (* z c)))
           (if (<= x -7e-248)
             t_1
             (if (<= x -7e-284)
               (* t (- (* i b) (* x a)))
               (if (<= x -1.16e-302)
                 t_3
                 (if (<= x 3e-230)
                   t_1
                   (if (<= x 3.3e+15)
                     t_3
                     (if (<= x 8.2e+80) t_1 t_2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double t_2 = x * ((y * z) - (a * t));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (x <= -1.04e+52) {
		tmp = t_2;
	} else if (x <= -1.45e-93) {
		tmp = y * ((x * z) - (j * i));
	} else if (x <= -1.22e-143) {
		tmp = a * ((j * c) - (x * t));
	} else if (x <= -1.35e-211) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= -7e-248) {
		tmp = t_1;
	} else if (x <= -7e-284) {
		tmp = t * ((i * b) - (x * a));
	} else if (x <= -1.16e-302) {
		tmp = t_3;
	} else if (x <= 3e-230) {
		tmp = t_1;
	} else if (x <= 3.3e+15) {
		tmp = t_3;
	} else if (x <= 8.2e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    t_2 = x * ((y * z) - (a * t))
    t_3 = i * ((t * b) - (y * j))
    if (x <= (-1.04d+52)) then
        tmp = t_2
    else if (x <= (-1.45d-93)) then
        tmp = y * ((x * z) - (j * i))
    else if (x <= (-1.22d-143)) then
        tmp = a * ((j * c) - (x * t))
    else if (x <= (-1.35d-211)) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= (-7d-248)) then
        tmp = t_1
    else if (x <= (-7d-284)) then
        tmp = t * ((i * b) - (x * a))
    else if (x <= (-1.16d-302)) then
        tmp = t_3
    else if (x <= 3d-230) then
        tmp = t_1
    else if (x <= 3.3d+15) then
        tmp = t_3
    else if (x <= 8.2d+80) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double t_2 = x * ((y * z) - (a * t));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (x <= -1.04e+52) {
		tmp = t_2;
	} else if (x <= -1.45e-93) {
		tmp = y * ((x * z) - (j * i));
	} else if (x <= -1.22e-143) {
		tmp = a * ((j * c) - (x * t));
	} else if (x <= -1.35e-211) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= -7e-248) {
		tmp = t_1;
	} else if (x <= -7e-284) {
		tmp = t * ((i * b) - (x * a));
	} else if (x <= -1.16e-302) {
		tmp = t_3;
	} else if (x <= 3e-230) {
		tmp = t_1;
	} else if (x <= 3.3e+15) {
		tmp = t_3;
	} else if (x <= 8.2e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = x * ((y * z) - (a * t))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if x <= -1.04e+52:
		tmp = t_2
	elif x <= -1.45e-93:
		tmp = y * ((x * z) - (j * i))
	elif x <= -1.22e-143:
		tmp = a * ((j * c) - (x * t))
	elif x <= -1.35e-211:
		tmp = b * ((t * i) - (z * c))
	elif x <= -7e-248:
		tmp = t_1
	elif x <= -7e-284:
		tmp = t * ((i * b) - (x * a))
	elif x <= -1.16e-302:
		tmp = t_3
	elif x <= 3e-230:
		tmp = t_1
	elif x <= 3.3e+15:
		tmp = t_3
	elif x <= 8.2e+80:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(a * t)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (x <= -1.04e+52)
		tmp = t_2;
	elseif (x <= -1.45e-93)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(j * i)));
	elseif (x <= -1.22e-143)
		tmp = Float64(a * Float64(Float64(j * c) - Float64(x * t)));
	elseif (x <= -1.35e-211)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= -7e-248)
		tmp = t_1;
	elseif (x <= -7e-284)
		tmp = Float64(t * Float64(Float64(i * b) - Float64(x * a)));
	elseif (x <= -1.16e-302)
		tmp = t_3;
	elseif (x <= 3e-230)
		tmp = t_1;
	elseif (x <= 3.3e+15)
		tmp = t_3;
	elseif (x <= 8.2e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	t_2 = x * ((y * z) - (a * t));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (x <= -1.04e+52)
		tmp = t_2;
	elseif (x <= -1.45e-93)
		tmp = y * ((x * z) - (j * i));
	elseif (x <= -1.22e-143)
		tmp = a * ((j * c) - (x * t));
	elseif (x <= -1.35e-211)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= -7e-248)
		tmp = t_1;
	elseif (x <= -7e-284)
		tmp = t * ((i * b) - (x * a));
	elseif (x <= -1.16e-302)
		tmp = t_3;
	elseif (x <= 3e-230)
		tmp = t_1;
	elseif (x <= 3.3e+15)
		tmp = t_3;
	elseif (x <= 8.2e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.04e+52], t$95$2, If[LessEqual[x, -1.45e-93], N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.22e-143], N[(a * N[(N[(j * c), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e-211], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7e-248], t$95$1, If[LessEqual[x, -7e-284], N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.16e-302], t$95$3, If[LessEqual[x, 3e-230], t$95$1, If[LessEqual[x, 3.3e+15], t$95$3, If[LessEqual[x, 8.2e+80], t$95$1, t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.04e52 or 8.20000000000000003e80 < x

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.04e52 < x < -1.4499999999999999e-93

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.4499999999999999e-93 < x < -1.22e-143

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.22e-143 < x < -1.35e-211

   1. Initial program 47.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.35e-211 < x < -6.99999999999999966e-248 or -1.16000000000000006e-302 < x < 3e-230 or 3.3e15 < x < 8.20000000000000003e80

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.99999999999999966e-248 < x < -6.99999999999999951e-284

   1. Initial program 99.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.99999999999999951e-284 < x < -1.16000000000000006e-302 or 3e-230 < x < 3.3e15

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 7 regimes into one program.
4. Add Preprocessing

Alternative 3: 30.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := -i \cdot \left(y \cdot j\right)\\ t_3 := \left(0 - x\right) \cdot \left(a \cdot t\right)\\ \mathbf{if}\;j \leq -5.8 \cdot 10^{+247}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.6 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-202}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-276}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{-224}:\\ \;\;\;\;\left(t \cdot b\right) \cdot i\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-117}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+54}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{+190}:\\ \;\;\;\;-\left(i \cdot j\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j)))
        (t_2 (- (* i (* y j))))
        (t_3 (* (- 0.0 x) (* a t))))
   (if (<= j -5.8e+247)
     t_2
     (if (<= j -6.2e+148)
       t_1
       (if (<= j -4.6e+94)
         t_2
         (if (<= j -5.2e-202)
           t_3
           (if (<= j -8.2e-276)
             (* z (- (* b c)))
             (if (<= j 6.8e-224)
               (* (* t b) i)
               (if (<= j 4.8e-117)
                 (* z (* x y))
                 (if (<= j 1.45e+54)
                   t_3
                   (if (<= j 1.8e+190) (- (* (* i j) y)) t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = -(i * (y * j));
	double t_3 = (0.0 - x) * (a * t);
	double tmp;
	if (j <= -5.8e+247) {
		tmp = t_2;
	} else if (j <= -6.2e+148) {
		tmp = t_1;
	} else if (j <= -4.6e+94) {
		tmp = t_2;
	} else if (j <= -5.2e-202) {
		tmp = t_3;
	} else if (j <= -8.2e-276) {
		tmp = z * -(b * c);
	} else if (j <= 6.8e-224) {
		tmp = (t * b) * i;
	} else if (j <= 4.8e-117) {
		tmp = z * (x * y);
	} else if (j <= 1.45e+54) {
		tmp = t_3;
	} else if (j <= 1.8e+190) {
		tmp = -((i * j) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = -(i * (y * j))
    t_3 = (0.0d0 - x) * (a * t)
    if (j <= (-5.8d+247)) then
        tmp = t_2
    else if (j <= (-6.2d+148)) then
        tmp = t_1
    else if (j <= (-4.6d+94)) then
        tmp = t_2
    else if (j <= (-5.2d-202)) then
        tmp = t_3
    else if (j <= (-8.2d-276)) then
        tmp = z * -(b * c)
    else if (j <= 6.8d-224) then
        tmp = (t * b) * i
    else if (j <= 4.8d-117) then
        tmp = z * (x * y)
    else if (j <= 1.45d+54) then
        tmp = t_3
    else if (j <= 1.8d+190) then
        tmp = -((i * j) * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = -(i * (y * j));
	double t_3 = (0.0 - x) * (a * t);
	double tmp;
	if (j <= -5.8e+247) {
		tmp = t_2;
	} else if (j <= -6.2e+148) {
		tmp = t_1;
	} else if (j <= -4.6e+94) {
		tmp = t_2;
	} else if (j <= -5.2e-202) {
		tmp = t_3;
	} else if (j <= -8.2e-276) {
		tmp = z * -(b * c);
	} else if (j <= 6.8e-224) {
		tmp = (t * b) * i;
	} else if (j <= 4.8e-117) {
		tmp = z * (x * y);
	} else if (j <= 1.45e+54) {
		tmp = t_3;
	} else if (j <= 1.8e+190) {
		tmp = -((i * j) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = -(i * (y * j))
	t_3 = (0.0 - x) * (a * t)
	tmp = 0
	if j <= -5.8e+247:
		tmp = t_2
	elif j <= -6.2e+148:
		tmp = t_1
	elif j <= -4.6e+94:
		tmp = t_2
	elif j <= -5.2e-202:
		tmp = t_3
	elif j <= -8.2e-276:
		tmp = z * -(b * c)
	elif j <= 6.8e-224:
		tmp = (t * b) * i
	elif j <= 4.8e-117:
		tmp = z * (x * y)
	elif j <= 1.45e+54:
		tmp = t_3
	elif j <= 1.8e+190:
		tmp = -((i * j) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(-Float64(i * Float64(y * j)))
	t_3 = Float64(Float64(0.0 - x) * Float64(a * t))
	tmp = 0.0
	if (j <= -5.8e+247)
		tmp = t_2;
	elseif (j <= -6.2e+148)
		tmp = t_1;
	elseif (j <= -4.6e+94)
		tmp = t_2;
	elseif (j <= -5.2e-202)
		tmp = t_3;
	elseif (j <= -8.2e-276)
		tmp = Float64(z * Float64(-Float64(b * c)));
	elseif (j <= 6.8e-224)
		tmp = Float64(Float64(t * b) * i);
	elseif (j <= 4.8e-117)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 1.45e+54)
		tmp = t_3;
	elseif (j <= 1.8e+190)
		tmp = Float64(-Float64(Float64(i * j) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = -(i * (y * j));
	t_3 = (0.0 - x) * (a * t);
	tmp = 0.0;
	if (j <= -5.8e+247)
		tmp = t_2;
	elseif (j <= -6.2e+148)
		tmp = t_1;
	elseif (j <= -4.6e+94)
		tmp = t_2;
	elseif (j <= -5.2e-202)
		tmp = t_3;
	elseif (j <= -8.2e-276)
		tmp = z * -(b * c);
	elseif (j <= 6.8e-224)
		tmp = (t * b) * i;
	elseif (j <= 4.8e-117)
		tmp = z * (x * y);
	elseif (j <= 1.45e+54)
		tmp = t_3;
	elseif (j <= 1.8e+190)
		tmp = -((i * j) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = (-N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision])}, Block[{t$95$3 = N[(N[(0.0 - x), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.8e+247], t$95$2, If[LessEqual[j, -6.2e+148], t$95$1, If[LessEqual[j, -4.6e+94], t$95$2, If[LessEqual[j, -5.2e-202], t$95$3, If[LessEqual[j, -8.2e-276], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[j, 6.8e-224], N[(N[(t * b), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[j, 4.8e-117], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.45e+54], t$95$3, If[LessEqual[j, 1.8e+190], (-N[(N[(i * j), $MachinePrecision] * y), $MachinePrecision]), t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -5.8000000000000004e247 or -6.19999999999999951e148 < j < -4.5999999999999999e94

   1. Initial program 62.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -5.8000000000000004e247 < j < -6.19999999999999951e148 or 1.79999999999999989e190 < j

   1. Initial program 51.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -4.5999999999999999e94 < j < -5.20000000000000019e-202 or 4.80000000000000028e-117 < j < 1.4499999999999999e54

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in j around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]

   if -5.20000000000000019e-202 < j < -8.2e-276

   1. Initial program 69.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -8.2e-276 < j < 6.79999999999999984e-224

   1. Initial program 91.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 6.79999999999999984e-224 < j < 4.80000000000000028e-117

   1. Initial program 59.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 1.4499999999999999e54 < j < 1.79999999999999989e190

   1. Initial program 67.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 7 regimes into one program.
4. Add Preprocessing

Alternative 4: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - a \cdot t\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -7 \cdot 10^{+128}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -45000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-288}:\\ \;\;\;\;\left(i \cdot t\right) \cdot \left(b - \frac{a \cdot x}{i}\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-33}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - \frac{i \cdot y}{a}\right)\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* a t)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -7e+128)
     t_2
     (if (<= c -45000000000.0)
       t_1
       (if (<= c -9e-288)
         (* (* i t) (- b (/ (* a x) i)))
         (if (<= c 5.5e-85)
           (* y (- (* x z) (* j i)))
           (if (<= c 1.15e-33)
             (* i (- (* t b) (* y j)))
             (if (<= c 1e+60)
               t_1
               (if (<= c 3.5e+114)
                 (* a (* j (- c (/ (* i y) a))))
                 (if (<= c 5e+156) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (a * t));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -7e+128) {
		tmp = t_2;
	} else if (c <= -45000000000.0) {
		tmp = t_1;
	} else if (c <= -9e-288) {
		tmp = (i * t) * (b - ((a * x) / i));
	} else if (c <= 5.5e-85) {
		tmp = y * ((x * z) - (j * i));
	} else if (c <= 1.15e-33) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 1e+60) {
		tmp = t_1;
	} else if (c <= 3.5e+114) {
		tmp = a * (j * (c - ((i * y) / a)));
	} else if (c <= 5e+156) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (a * t))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-7d+128)) then
        tmp = t_2
    else if (c <= (-45000000000.0d0)) then
        tmp = t_1
    else if (c <= (-9d-288)) then
        tmp = (i * t) * (b - ((a * x) / i))
    else if (c <= 5.5d-85) then
        tmp = y * ((x * z) - (j * i))
    else if (c <= 1.15d-33) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= 1d+60) then
        tmp = t_1
    else if (c <= 3.5d+114) then
        tmp = a * (j * (c - ((i * y) / a)))
    else if (c <= 5d+156) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (a * t));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -7e+128) {
		tmp = t_2;
	} else if (c <= -45000000000.0) {
		tmp = t_1;
	} else if (c <= -9e-288) {
		tmp = (i * t) * (b - ((a * x) / i));
	} else if (c <= 5.5e-85) {
		tmp = y * ((x * z) - (j * i));
	} else if (c <= 1.15e-33) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 1e+60) {
		tmp = t_1;
	} else if (c <= 3.5e+114) {
		tmp = a * (j * (c - ((i * y) / a)));
	} else if (c <= 5e+156) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (a * t))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -7e+128:
		tmp = t_2
	elif c <= -45000000000.0:
		tmp = t_1
	elif c <= -9e-288:
		tmp = (i * t) * (b - ((a * x) / i))
	elif c <= 5.5e-85:
		tmp = y * ((x * z) - (j * i))
	elif c <= 1.15e-33:
		tmp = i * ((t * b) - (y * j))
	elif c <= 1e+60:
		tmp = t_1
	elif c <= 3.5e+114:
		tmp = a * (j * (c - ((i * y) / a)))
	elif c <= 5e+156:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(a * t)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -7e+128)
		tmp = t_2;
	elseif (c <= -45000000000.0)
		tmp = t_1;
	elseif (c <= -9e-288)
		tmp = Float64(Float64(i * t) * Float64(b - Float64(Float64(a * x) / i)));
	elseif (c <= 5.5e-85)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(j * i)));
	elseif (c <= 1.15e-33)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= 1e+60)
		tmp = t_1;
	elseif (c <= 3.5e+114)
		tmp = Float64(a * Float64(j * Float64(c - Float64(Float64(i * y) / a))));
	elseif (c <= 5e+156)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (a * t));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -7e+128)
		tmp = t_2;
	elseif (c <= -45000000000.0)
		tmp = t_1;
	elseif (c <= -9e-288)
		tmp = (i * t) * (b - ((a * x) / i));
	elseif (c <= 5.5e-85)
		tmp = y * ((x * z) - (j * i));
	elseif (c <= 1.15e-33)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= 1e+60)
		tmp = t_1;
	elseif (c <= 3.5e+114)
		tmp = a * (j * (c - ((i * y) / a)));
	elseif (c <= 5e+156)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7e+128], t$95$2, If[LessEqual[c, -45000000000.0], t$95$1, If[LessEqual[c, -9e-288], N[(N[(i * t), $MachinePrecision] * N[(b - N[(N[(a * x), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.5e-85], N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e-33], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1e+60], t$95$1, If[LessEqual[c, 3.5e+114], N[(a * N[(j * N[(c - N[(N[(i * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5e+156], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -6.99999999999999937e128 or 4.99999999999999992e156 < c

   1. Initial program 59.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.99999999999999937e128 < c < -4.5e10 or 1.14999999999999993e-33 < c < 9.9999999999999995e59 or 3.5000000000000001e114 < c < 4.99999999999999992e156

   1. Initial program 62.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.5e10 < c < -9.0000000000000003e-288

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -9.0000000000000003e-288 < c < 5.4999999999999997e-85

   1. Initial program 78.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 5.4999999999999997e-85 < c < 1.14999999999999993e-33

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 9.9999999999999995e59 < c < 3.5000000000000001e114

   1. Initial program 54.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 5: 53.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b - a \cdot x\right) - i \cdot \left(j \cdot y\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -780:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-281}:\\ \;\;\;\;\left(i \cdot t\right) \cdot \left(b - \frac{a \cdot x}{i}\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t (- (* i b) (* a x))) (* i (* j y))))
        (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -1.15e+135)
     t_2
     (if (<= c -780.0)
       t_1
       (if (<= c -2.05e-281)
         (* (* i t) (- b (/ (* a x) i)))
         (if (<= c 2.9e-307)
           t_1
           (if (<= c 2.1e-170)
             (* y (- (* x z) (* j i)))
             (if (<= c 1.85e+164) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * ((i * b) - (a * x))) - (i * (j * y));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.15e+135) {
		tmp = t_2;
	} else if (c <= -780.0) {
		tmp = t_1;
	} else if (c <= -2.05e-281) {
		tmp = (i * t) * (b - ((a * x) / i));
	} else if (c <= 2.9e-307) {
		tmp = t_1;
	} else if (c <= 2.1e-170) {
		tmp = y * ((x * z) - (j * i));
	} else if (c <= 1.85e+164) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * ((i * b) - (a * x))) - (i * (j * y))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-1.15d+135)) then
        tmp = t_2
    else if (c <= (-780.0d0)) then
        tmp = t_1
    else if (c <= (-2.05d-281)) then
        tmp = (i * t) * (b - ((a * x) / i))
    else if (c <= 2.9d-307) then
        tmp = t_1
    else if (c <= 2.1d-170) then
        tmp = y * ((x * z) - (j * i))
    else if (c <= 1.85d+164) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * ((i * b) - (a * x))) - (i * (j * y));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.15e+135) {
		tmp = t_2;
	} else if (c <= -780.0) {
		tmp = t_1;
	} else if (c <= -2.05e-281) {
		tmp = (i * t) * (b - ((a * x) / i));
	} else if (c <= 2.9e-307) {
		tmp = t_1;
	} else if (c <= 2.1e-170) {
		tmp = y * ((x * z) - (j * i));
	} else if (c <= 1.85e+164) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * ((i * b) - (a * x))) - (i * (j * y))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.15e+135:
		tmp = t_2
	elif c <= -780.0:
		tmp = t_1
	elif c <= -2.05e-281:
		tmp = (i * t) * (b - ((a * x) / i))
	elif c <= 2.9e-307:
		tmp = t_1
	elif c <= 2.1e-170:
		tmp = y * ((x * z) - (j * i))
	elif c <= 1.85e+164:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * Float64(Float64(i * b) - Float64(a * x))) - Float64(i * Float64(j * y)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.15e+135)
		tmp = t_2;
	elseif (c <= -780.0)
		tmp = t_1;
	elseif (c <= -2.05e-281)
		tmp = Float64(Float64(i * t) * Float64(b - Float64(Float64(a * x) / i)));
	elseif (c <= 2.9e-307)
		tmp = t_1;
	elseif (c <= 2.1e-170)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(j * i)));
	elseif (c <= 1.85e+164)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * ((i * b) - (a * x))) - (i * (j * y));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.15e+135)
		tmp = t_2;
	elseif (c <= -780.0)
		tmp = t_1;
	elseif (c <= -2.05e-281)
		tmp = (i * t) * (b - ((a * x) / i));
	elseif (c <= 2.9e-307)
		tmp = t_1;
	elseif (c <= 2.1e-170)
		tmp = y * ((x * z) - (j * i));
	elseif (c <= 1.85e+164)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * N[(N[(i * b), $MachinePrecision] - N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+135], t$95$2, If[LessEqual[c, -780.0], t$95$1, If[LessEqual[c, -2.05e-281], N[(N[(i * t), $MachinePrecision] * N[(b - N[(N[(a * x), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.9e-307], t$95$1, If[LessEqual[c, 2.1e-170], N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.85e+164], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.1500000000000001e135 or 1.85e164 < c

   1. Initial program 58.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.1500000000000001e135 < c < -780 or -2.05e-281 < c < 2.9e-307 or 2.1000000000000001e-170 < c < 1.85e164

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -780 < c < -2.05e-281

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 2.9e-307 < c < 2.1000000000000001e-170

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 29.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -b \cdot \left(z \cdot c\right)\\ t_2 := \left(t \cdot b\right) \cdot i\\ t_3 := a \cdot \left(-x \cdot t\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+221}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-109}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-302}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (* z c)))) (t_2 (* (* t b) i)) (t_3 (* a (- (* x t)))))
   (if (<= x -3.2e+221)
     t_3
     (if (<= x -1.3e-109)
       (* y (* x z))
       (if (<= x -3.8e-302)
         t_2
         (if (<= x 1.02e-255)
           t_1
           (if (<= x 1.7e-134)
             t_2
             (if (<= x 4.8e-77) t_1 (if (<= x 3.7e+93) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -(b * (z * c));
	double t_2 = (t * b) * i;
	double t_3 = a * -(x * t);
	double tmp;
	if (x <= -3.2e+221) {
		tmp = t_3;
	} else if (x <= -1.3e-109) {
		tmp = y * (x * z);
	} else if (x <= -3.8e-302) {
		tmp = t_2;
	} else if (x <= 1.02e-255) {
		tmp = t_1;
	} else if (x <= 1.7e-134) {
		tmp = t_2;
	} else if (x <= 4.8e-77) {
		tmp = t_1;
	} else if (x <= 3.7e+93) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = -(b * (z * c))
    t_2 = (t * b) * i
    t_3 = a * -(x * t)
    if (x <= (-3.2d+221)) then
        tmp = t_3
    else if (x <= (-1.3d-109)) then
        tmp = y * (x * z)
    else if (x <= (-3.8d-302)) then
        tmp = t_2
    else if (x <= 1.02d-255) then
        tmp = t_1
    else if (x <= 1.7d-134) then
        tmp = t_2
    else if (x <= 4.8d-77) then
        tmp = t_1
    else if (x <= 3.7d+93) then
        tmp = t_2
    else
        tmp = t_3
    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 t_1 = -(b * (z * c));
	double t_2 = (t * b) * i;
	double t_3 = a * -(x * t);
	double tmp;
	if (x <= -3.2e+221) {
		tmp = t_3;
	} else if (x <= -1.3e-109) {
		tmp = y * (x * z);
	} else if (x <= -3.8e-302) {
		tmp = t_2;
	} else if (x <= 1.02e-255) {
		tmp = t_1;
	} else if (x <= 1.7e-134) {
		tmp = t_2;
	} else if (x <= 4.8e-77) {
		tmp = t_1;
	} else if (x <= 3.7e+93) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -(b * (z * c))
	t_2 = (t * b) * i
	t_3 = a * -(x * t)
	tmp = 0
	if x <= -3.2e+221:
		tmp = t_3
	elif x <= -1.3e-109:
		tmp = y * (x * z)
	elif x <= -3.8e-302:
		tmp = t_2
	elif x <= 1.02e-255:
		tmp = t_1
	elif x <= 1.7e-134:
		tmp = t_2
	elif x <= 4.8e-77:
		tmp = t_1
	elif x <= 3.7e+93:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(-Float64(b * Float64(z * c)))
	t_2 = Float64(Float64(t * b) * i)
	t_3 = Float64(a * Float64(-Float64(x * t)))
	tmp = 0.0
	if (x <= -3.2e+221)
		tmp = t_3;
	elseif (x <= -1.3e-109)
		tmp = Float64(y * Float64(x * z));
	elseif (x <= -3.8e-302)
		tmp = t_2;
	elseif (x <= 1.02e-255)
		tmp = t_1;
	elseif (x <= 1.7e-134)
		tmp = t_2;
	elseif (x <= 4.8e-77)
		tmp = t_1;
	elseif (x <= 3.7e+93)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -(b * (z * c));
	t_2 = (t * b) * i;
	t_3 = a * -(x * t);
	tmp = 0.0;
	if (x <= -3.2e+221)
		tmp = t_3;
	elseif (x <= -1.3e-109)
		tmp = y * (x * z);
	elseif (x <= -3.8e-302)
		tmp = t_2;
	elseif (x <= 1.02e-255)
		tmp = t_1;
	elseif (x <= 1.7e-134)
		tmp = t_2;
	elseif (x <= 4.8e-77)
		tmp = t_1;
	elseif (x <= 3.7e+93)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = (-N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision])}, Block[{t$95$2 = N[(N[(t * b), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$3 = N[(a * (-N[(x * t), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[x, -3.2e+221], t$95$3, If[LessEqual[x, -1.3e-109], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.8e-302], t$95$2, If[LessEqual[x, 1.02e-255], t$95$1, If[LessEqual[x, 1.7e-134], t$95$2, If[LessEqual[x, 4.8e-77], t$95$1, If[LessEqual[x, 3.7e+93], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.2e221 or 3.69999999999999987e93 < x

   1. Initial program 63.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in j around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -3.2e221 < x < -1.2999999999999999e-109

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.2999999999999999e-109 < x < -3.8e-302 or 1.02000000000000002e-255 < x < 1.69999999999999988e-134 or 4.7999999999999998e-77 < x < 3.69999999999999987e93

   1. Initial program 68.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -3.8e-302 < x < 1.02000000000000002e-255 or 1.69999999999999988e-134 < x < 4.7999999999999998e-77

   1. Initial program 76.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - c \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z - a \cdot t\right)\\ t_3 := a \cdot \left(j \cdot \left(c - \frac{i \cdot y}{a}\right)\right)\\ \mathbf{if}\;j \leq -1.8 \cdot 10^{+114}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-206}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* c b))))
        (t_2 (* x (- (* y z) (* a t))))
        (t_3 (* a (* j (- c (/ (* i y) a))))))
   (if (<= j -1.8e+114)
     t_3
     (if (<= j -5.2e-206)
       t_2
       (if (<= j -1.95e-284)
         t_1
         (if (<= j 1.75e-219)
           (* t (- (* i b) (* x a)))
           (if (<= j 7.4e-117) t_1 (if (<= j 5e+24) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (c * b));
	double t_2 = x * ((y * z) - (a * t));
	double t_3 = a * (j * (c - ((i * y) / a)));
	double tmp;
	if (j <= -1.8e+114) {
		tmp = t_3;
	} else if (j <= -5.2e-206) {
		tmp = t_2;
	} else if (j <= -1.95e-284) {
		tmp = t_1;
	} else if (j <= 1.75e-219) {
		tmp = t * ((i * b) - (x * a));
	} else if (j <= 7.4e-117) {
		tmp = t_1;
	} else if (j <= 5e+24) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * ((x * y) - (c * b))
    t_2 = x * ((y * z) - (a * t))
    t_3 = a * (j * (c - ((i * y) / a)))
    if (j <= (-1.8d+114)) then
        tmp = t_3
    else if (j <= (-5.2d-206)) then
        tmp = t_2
    else if (j <= (-1.95d-284)) then
        tmp = t_1
    else if (j <= 1.75d-219) then
        tmp = t * ((i * b) - (x * a))
    else if (j <= 7.4d-117) then
        tmp = t_1
    else if (j <= 5d+24) then
        tmp = t_2
    else
        tmp = t_3
    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 t_1 = z * ((x * y) - (c * b));
	double t_2 = x * ((y * z) - (a * t));
	double t_3 = a * (j * (c - ((i * y) / a)));
	double tmp;
	if (j <= -1.8e+114) {
		tmp = t_3;
	} else if (j <= -5.2e-206) {
		tmp = t_2;
	} else if (j <= -1.95e-284) {
		tmp = t_1;
	} else if (j <= 1.75e-219) {
		tmp = t * ((i * b) - (x * a));
	} else if (j <= 7.4e-117) {
		tmp = t_1;
	} else if (j <= 5e+24) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (c * b))
	t_2 = x * ((y * z) - (a * t))
	t_3 = a * (j * (c - ((i * y) / a)))
	tmp = 0
	if j <= -1.8e+114:
		tmp = t_3
	elif j <= -5.2e-206:
		tmp = t_2
	elif j <= -1.95e-284:
		tmp = t_1
	elif j <= 1.75e-219:
		tmp = t * ((i * b) - (x * a))
	elif j <= 7.4e-117:
		tmp = t_1
	elif j <= 5e+24:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(c * b)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(a * t)))
	t_3 = Float64(a * Float64(j * Float64(c - Float64(Float64(i * y) / a))))
	tmp = 0.0
	if (j <= -1.8e+114)
		tmp = t_3;
	elseif (j <= -5.2e-206)
		tmp = t_2;
	elseif (j <= -1.95e-284)
		tmp = t_1;
	elseif (j <= 1.75e-219)
		tmp = Float64(t * Float64(Float64(i * b) - Float64(x * a)));
	elseif (j <= 7.4e-117)
		tmp = t_1;
	elseif (j <= 5e+24)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (c * b));
	t_2 = x * ((y * z) - (a * t));
	t_3 = a * (j * (c - ((i * y) / a)));
	tmp = 0.0;
	if (j <= -1.8e+114)
		tmp = t_3;
	elseif (j <= -5.2e-206)
		tmp = t_2;
	elseif (j <= -1.95e-284)
		tmp = t_1;
	elseif (j <= 1.75e-219)
		tmp = t * ((i * b) - (x * a));
	elseif (j <= 7.4e-117)
		tmp = t_1;
	elseif (j <= 5e+24)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(j * N[(c - N[(N[(i * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.8e+114], t$95$3, If[LessEqual[j, -5.2e-206], t$95$2, If[LessEqual[j, -1.95e-284], t$95$1, If[LessEqual[j, 1.75e-219], N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.4e-117], t$95$1, If[LessEqual[j, 5e+24], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.8e114 or 5.00000000000000045e24 < j

   1. Initial program 59.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.8e114 < j < -5.2000000000000001e-206 or 7.4000000000000005e-117 < j < 5.00000000000000045e24

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.2000000000000001e-206 < j < -1.9499999999999999e-284 or 1.75000000000000006e-219 < j < 7.4000000000000005e-117

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.9499999999999999e-284 < j < 1.75000000000000006e-219

   1. Initial program 83.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 26.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;c \leq -2.2 \cdot 10^{+58}:\\ \;\;\;\;\left(a \cdot c\right) \cdot j\\ \mathbf{elif}\;c \leq -85000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -6.4 \cdot 10^{-288}:\\ \;\;\;\;\left(t \cdot b\right) \cdot i\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 6.3 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+109}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* y (* x z))))
   (if (<= c -2.2e+58)
     (* (* a c) j)
     (if (<= c -85000000000.0)
       t_1
       (if (<= c -6.4e-288)
         (* (* t b) i)
         (if (<= c 1.25e-85)
           t_2
           (if (<= c 6.3e+30)
             (* t (* i b))
             (if (<= c 5.1e+60)
               t_1
               (if (<= c 3.7e+109) (* a (* c j)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = y * (x * z);
	double tmp;
	if (c <= -2.2e+58) {
		tmp = (a * c) * j;
	} else if (c <= -85000000000.0) {
		tmp = t_1;
	} else if (c <= -6.4e-288) {
		tmp = (t * b) * i;
	} else if (c <= 1.25e-85) {
		tmp = t_2;
	} else if (c <= 6.3e+30) {
		tmp = t * (i * b);
	} else if (c <= 5.1e+60) {
		tmp = t_1;
	} else if (c <= 3.7e+109) {
		tmp = a * (c * j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = y * (x * z)
    if (c <= (-2.2d+58)) then
        tmp = (a * c) * j
    else if (c <= (-85000000000.0d0)) then
        tmp = t_1
    else if (c <= (-6.4d-288)) then
        tmp = (t * b) * i
    else if (c <= 1.25d-85) then
        tmp = t_2
    else if (c <= 6.3d+30) then
        tmp = t * (i * b)
    else if (c <= 5.1d+60) then
        tmp = t_1
    else if (c <= 3.7d+109) then
        tmp = a * (c * j)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = y * (x * z);
	double tmp;
	if (c <= -2.2e+58) {
		tmp = (a * c) * j;
	} else if (c <= -85000000000.0) {
		tmp = t_1;
	} else if (c <= -6.4e-288) {
		tmp = (t * b) * i;
	} else if (c <= 1.25e-85) {
		tmp = t_2;
	} else if (c <= 6.3e+30) {
		tmp = t * (i * b);
	} else if (c <= 5.1e+60) {
		tmp = t_1;
	} else if (c <= 3.7e+109) {
		tmp = a * (c * j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = y * (x * z)
	tmp = 0
	if c <= -2.2e+58:
		tmp = (a * c) * j
	elif c <= -85000000000.0:
		tmp = t_1
	elif c <= -6.4e-288:
		tmp = (t * b) * i
	elif c <= 1.25e-85:
		tmp = t_2
	elif c <= 6.3e+30:
		tmp = t * (i * b)
	elif c <= 5.1e+60:
		tmp = t_1
	elif c <= 3.7e+109:
		tmp = a * (c * j)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (c <= -2.2e+58)
		tmp = Float64(Float64(a * c) * j);
	elseif (c <= -85000000000.0)
		tmp = t_1;
	elseif (c <= -6.4e-288)
		tmp = Float64(Float64(t * b) * i);
	elseif (c <= 1.25e-85)
		tmp = t_2;
	elseif (c <= 6.3e+30)
		tmp = Float64(t * Float64(i * b));
	elseif (c <= 5.1e+60)
		tmp = t_1;
	elseif (c <= 3.7e+109)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = y * (x * z);
	tmp = 0.0;
	if (c <= -2.2e+58)
		tmp = (a * c) * j;
	elseif (c <= -85000000000.0)
		tmp = t_1;
	elseif (c <= -6.4e-288)
		tmp = (t * b) * i;
	elseif (c <= 1.25e-85)
		tmp = t_2;
	elseif (c <= 6.3e+30)
		tmp = t * (i * b);
	elseif (c <= 5.1e+60)
		tmp = t_1;
	elseif (c <= 3.7e+109)
		tmp = a * (c * j);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.2e+58], N[(N[(a * c), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[c, -85000000000.0], t$95$1, If[LessEqual[c, -6.4e-288], N[(N[(t * b), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[c, 1.25e-85], t$95$2, If[LessEqual[c, 6.3e+30], N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.1e+60], t$95$1, If[LessEqual[c, 3.7e+109], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -2.2000000000000001e58

   1. Initial program 53.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -2.2000000000000001e58 < c < -8.5e10 or 6.30000000000000004e30 < c < 5.09999999999999996e60

   1. Initial program 65.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -8.5e10 < c < -6.4000000000000001e-288

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -6.4000000000000001e-288 < c < 1.25e-85 or 3.7000000000000002e109 < c

   1. Initial program 70.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 1.25e-85 < c < 6.30000000000000004e30

   1. Initial program 86.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 5.09999999999999996e60 < c < 3.7000000000000002e109

   1. Initial program 54.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 9: 52.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - c \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z - a \cdot t\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.9 \cdot 10^{+113}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-207}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-285}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-218}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;j \leq 5.1 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 9.4 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* c b))))
        (t_2 (* x (- (* y z) (* a t))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -3.9e+113)
     t_3
     (if (<= j -2.9e-207)
       t_2
       (if (<= j -1.55e-285)
         t_1
         (if (<= j 3.4e-218)
           (* t (- (* i b) (* x a)))
           (if (<= j 5.1e-117) t_1 (if (<= j 9.4e+26) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (c * b));
	double t_2 = x * ((y * z) - (a * t));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.9e+113) {
		tmp = t_3;
	} else if (j <= -2.9e-207) {
		tmp = t_2;
	} else if (j <= -1.55e-285) {
		tmp = t_1;
	} else if (j <= 3.4e-218) {
		tmp = t * ((i * b) - (x * a));
	} else if (j <= 5.1e-117) {
		tmp = t_1;
	} else if (j <= 9.4e+26) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * ((x * y) - (c * b))
    t_2 = x * ((y * z) - (a * t))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-3.9d+113)) then
        tmp = t_3
    else if (j <= (-2.9d-207)) then
        tmp = t_2
    else if (j <= (-1.55d-285)) then
        tmp = t_1
    else if (j <= 3.4d-218) then
        tmp = t * ((i * b) - (x * a))
    else if (j <= 5.1d-117) then
        tmp = t_1
    else if (j <= 9.4d+26) then
        tmp = t_2
    else
        tmp = t_3
    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 t_1 = z * ((x * y) - (c * b));
	double t_2 = x * ((y * z) - (a * t));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.9e+113) {
		tmp = t_3;
	} else if (j <= -2.9e-207) {
		tmp = t_2;
	} else if (j <= -1.55e-285) {
		tmp = t_1;
	} else if (j <= 3.4e-218) {
		tmp = t * ((i * b) - (x * a));
	} else if (j <= 5.1e-117) {
		tmp = t_1;
	} else if (j <= 9.4e+26) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (c * b))
	t_2 = x * ((y * z) - (a * t))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -3.9e+113:
		tmp = t_3
	elif j <= -2.9e-207:
		tmp = t_2
	elif j <= -1.55e-285:
		tmp = t_1
	elif j <= 3.4e-218:
		tmp = t * ((i * b) - (x * a))
	elif j <= 5.1e-117:
		tmp = t_1
	elif j <= 9.4e+26:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(c * b)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(a * t)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.9e+113)
		tmp = t_3;
	elseif (j <= -2.9e-207)
		tmp = t_2;
	elseif (j <= -1.55e-285)
		tmp = t_1;
	elseif (j <= 3.4e-218)
		tmp = Float64(t * Float64(Float64(i * b) - Float64(x * a)));
	elseif (j <= 5.1e-117)
		tmp = t_1;
	elseif (j <= 9.4e+26)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (c * b));
	t_2 = x * ((y * z) - (a * t));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.9e+113)
		tmp = t_3;
	elseif (j <= -2.9e-207)
		tmp = t_2;
	elseif (j <= -1.55e-285)
		tmp = t_1;
	elseif (j <= 3.4e-218)
		tmp = t * ((i * b) - (x * a));
	elseif (j <= 5.1e-117)
		tmp = t_1;
	elseif (j <= 9.4e+26)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.9e+113], t$95$3, If[LessEqual[j, -2.9e-207], t$95$2, If[LessEqual[j, -1.55e-285], t$95$1, If[LessEqual[j, 3.4e-218], N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.1e-117], t$95$1, If[LessEqual[j, 9.4e+26], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.9000000000000002e113 or 9.3999999999999995e26 < j

   1. Initial program 59.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.9000000000000002e113 < j < -2.90000000000000011e-207 or 5.1000000000000002e-117 < j < 9.3999999999999995e26

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.90000000000000011e-207 < j < -1.55e-285 or 3.39999999999999986e-218 < j < 5.1000000000000002e-117

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.55e-285 < j < 3.39999999999999986e-218

   1. Initial program 83.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b - x \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + \frac{-b \cdot c}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* t (- (* i b) (* x a))) (* j (- (* c a) (* y i))))))
   (if (<= z -3.2e+112)
     (* z (- (* x y) (* c b)))
     (if (<= z 3.4e-66)
       t_1
       (if (<= z 2.1e+18)
         (* i (- (* t b) (* y j)))
         (if (<= z 1.15e+111) t_1 (* z (* x (+ y (/ (- (* b c)) x))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * ((i * b) - (x * a))) + (j * ((c * a) - (y * i)));
	double tmp;
	if (z <= -3.2e+112) {
		tmp = z * ((x * y) - (c * b));
	} else if (z <= 3.4e-66) {
		tmp = t_1;
	} else if (z <= 2.1e+18) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 1.15e+111) {
		tmp = t_1;
	} else {
		tmp = z * (x * (y + (-(b * c) / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = (t * ((i * b) - (x * a))) + (j * ((c * a) - (y * i)))
    if (z <= (-3.2d+112)) then
        tmp = z * ((x * y) - (c * b))
    else if (z <= 3.4d-66) then
        tmp = t_1
    else if (z <= 2.1d+18) then
        tmp = i * ((t * b) - (y * j))
    else if (z <= 1.15d+111) then
        tmp = t_1
    else
        tmp = z * (x * (y + (-(b * c) / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * ((i * b) - (x * a))) + (j * ((c * a) - (y * i)));
	double tmp;
	if (z <= -3.2e+112) {
		tmp = z * ((x * y) - (c * b));
	} else if (z <= 3.4e-66) {
		tmp = t_1;
	} else if (z <= 2.1e+18) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 1.15e+111) {
		tmp = t_1;
	} else {
		tmp = z * (x * (y + (-(b * c) / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * ((i * b) - (x * a))) + (j * ((c * a) - (y * i)))
	tmp = 0
	if z <= -3.2e+112:
		tmp = z * ((x * y) - (c * b))
	elif z <= 3.4e-66:
		tmp = t_1
	elif z <= 2.1e+18:
		tmp = i * ((t * b) - (y * j))
	elif z <= 1.15e+111:
		tmp = t_1
	else:
		tmp = z * (x * (y + (-(b * c) / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * Float64(Float64(i * b) - Float64(x * a))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
	tmp = 0.0
	if (z <= -3.2e+112)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(c * b)));
	elseif (z <= 3.4e-66)
		tmp = t_1;
	elseif (z <= 2.1e+18)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (z <= 1.15e+111)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x * Float64(y + Float64(Float64(-Float64(b * c)) / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * ((i * b) - (x * a))) + (j * ((c * a) - (y * i)));
	tmp = 0.0;
	if (z <= -3.2e+112)
		tmp = z * ((x * y) - (c * b));
	elseif (z <= 3.4e-66)
		tmp = t_1;
	elseif (z <= 2.1e+18)
		tmp = i * ((t * b) - (y * j));
	elseif (z <= 1.15e+111)
		tmp = t_1;
	else
		tmp = z * (x * (y + (-(b * c) / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+112], N[(z * N[(N[(x * y), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-66], t$95$1, If[LessEqual[z, 2.1e+18], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+111], t$95$1, N[(z * N[(x * N[(y + N[((-N[(b * c), $MachinePrecision]) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.19999999999999986e112

   1. Initial program 69.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.19999999999999986e112 < z < 3.39999999999999997e-66 or 2.1e18 < z < 1.15000000000000001e111

   1. Initial program 73.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 3.39999999999999997e-66 < z < 2.1e18

   1. Initial program 61.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.15000000000000001e111 < z

   1. Initial program 61.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 52.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - j \cdot i\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;t \leq -3.15 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-167}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(\frac{i \cdot b}{a} - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* j i)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= t -3.15e+72)
     (* t (- (* i b) (* x a)))
     (if (<= t -2.75e-50)
       t_2
       (if (<= t -1.8e-300)
         t_1
         (if (<= t 6.4e-167)
           t_2
           (if (<= t 3.8e-32) t_1 (* t (* a (- (/ (* i b) a) x))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (j * i));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (t <= -3.15e+72) {
		tmp = t * ((i * b) - (x * a));
	} else if (t <= -2.75e-50) {
		tmp = t_2;
	} else if (t <= -1.8e-300) {
		tmp = t_1;
	} else if (t <= 6.4e-167) {
		tmp = t_2;
	} else if (t <= 3.8e-32) {
		tmp = t_1;
	} else {
		tmp = t * (a * (((i * b) / a) - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((x * z) - (j * i))
    t_2 = c * ((a * j) - (z * b))
    if (t <= (-3.15d+72)) then
        tmp = t * ((i * b) - (x * a))
    else if (t <= (-2.75d-50)) then
        tmp = t_2
    else if (t <= (-1.8d-300)) then
        tmp = t_1
    else if (t <= 6.4d-167) then
        tmp = t_2
    else if (t <= 3.8d-32) then
        tmp = t_1
    else
        tmp = t * (a * (((i * b) / a) - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (j * i));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (t <= -3.15e+72) {
		tmp = t * ((i * b) - (x * a));
	} else if (t <= -2.75e-50) {
		tmp = t_2;
	} else if (t <= -1.8e-300) {
		tmp = t_1;
	} else if (t <= 6.4e-167) {
		tmp = t_2;
	} else if (t <= 3.8e-32) {
		tmp = t_1;
	} else {
		tmp = t * (a * (((i * b) / a) - x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (j * i))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if t <= -3.15e+72:
		tmp = t * ((i * b) - (x * a))
	elif t <= -2.75e-50:
		tmp = t_2
	elif t <= -1.8e-300:
		tmp = t_1
	elif t <= 6.4e-167:
		tmp = t_2
	elif t <= 3.8e-32:
		tmp = t_1
	else:
		tmp = t * (a * (((i * b) / a) - x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(j * i)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (t <= -3.15e+72)
		tmp = Float64(t * Float64(Float64(i * b) - Float64(x * a)));
	elseif (t <= -2.75e-50)
		tmp = t_2;
	elseif (t <= -1.8e-300)
		tmp = t_1;
	elseif (t <= 6.4e-167)
		tmp = t_2;
	elseif (t <= 3.8e-32)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(a * Float64(Float64(Float64(i * b) / a) - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (j * i));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (t <= -3.15e+72)
		tmp = t * ((i * b) - (x * a));
	elseif (t <= -2.75e-50)
		tmp = t_2;
	elseif (t <= -1.8e-300)
		tmp = t_1;
	elseif (t <= 6.4e-167)
		tmp = t_2;
	elseif (t <= 3.8e-32)
		tmp = t_1;
	else
		tmp = t * (a * (((i * b) / a) - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.15e+72], N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.75e-50], t$95$2, If[LessEqual[t, -1.8e-300], t$95$1, If[LessEqual[t, 6.4e-167], t$95$2, If[LessEqual[t, 3.8e-32], t$95$1, N[(t * N[(a * N[(N[(N[(i * b), $MachinePrecision] / a), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.14999999999999981e72

   1. Initial program 55.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.14999999999999981e72 < t < -2.74999999999999987e-50 or -1.80000000000000008e-300 < t < 6.4000000000000003e-167

   1. Initial program 74.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.74999999999999987e-50 < t < -1.80000000000000008e-300 or 6.4000000000000003e-167 < t < 3.80000000000000008e-32

   1. Initial program 79.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 3.80000000000000008e-32 < t

   1. Initial program 66.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 12: 52.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-302}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 72000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b))))
        (t_2 (* i (- (* t b) (* y j))))
        (t_3 (* x (- (* y z) (* a t)))))
   (if (<= x -6.2e+45)
     t_3
     (if (<= x -4.6e-302)
       t_2
       (if (<= x 7.5e-229)
         t_1
         (if (<= x 72000000000.0) t_2 (if (<= x 9.5e+85) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = x * ((y * z) - (a * t));
	double tmp;
	if (x <= -6.2e+45) {
		tmp = t_3;
	} else if (x <= -4.6e-302) {
		tmp = t_2;
	} else if (x <= 7.5e-229) {
		tmp = t_1;
	} else if (x <= 72000000000.0) {
		tmp = t_2;
	} else if (x <= 9.5e+85) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    t_2 = i * ((t * b) - (y * j))
    t_3 = x * ((y * z) - (a * t))
    if (x <= (-6.2d+45)) then
        tmp = t_3
    else if (x <= (-4.6d-302)) then
        tmp = t_2
    else if (x <= 7.5d-229) then
        tmp = t_1
    else if (x <= 72000000000.0d0) then
        tmp = t_2
    else if (x <= 9.5d+85) then
        tmp = t_1
    else
        tmp = t_3
    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 t_1 = c * ((a * j) - (z * b));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = x * ((y * z) - (a * t));
	double tmp;
	if (x <= -6.2e+45) {
		tmp = t_3;
	} else if (x <= -4.6e-302) {
		tmp = t_2;
	} else if (x <= 7.5e-229) {
		tmp = t_1;
	} else if (x <= 72000000000.0) {
		tmp = t_2;
	} else if (x <= 9.5e+85) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = i * ((t * b) - (y * j))
	t_3 = x * ((y * z) - (a * t))
	tmp = 0
	if x <= -6.2e+45:
		tmp = t_3
	elif x <= -4.6e-302:
		tmp = t_2
	elif x <= 7.5e-229:
		tmp = t_1
	elif x <= 72000000000.0:
		tmp = t_2
	elif x <= 9.5e+85:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(a * t)))
	tmp = 0.0
	if (x <= -6.2e+45)
		tmp = t_3;
	elseif (x <= -4.6e-302)
		tmp = t_2;
	elseif (x <= 7.5e-229)
		tmp = t_1;
	elseif (x <= 72000000000.0)
		tmp = t_2;
	elseif (x <= 9.5e+85)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	t_2 = i * ((t * b) - (y * j));
	t_3 = x * ((y * z) - (a * t));
	tmp = 0.0;
	if (x <= -6.2e+45)
		tmp = t_3;
	elseif (x <= -4.6e-302)
		tmp = t_2;
	elseif (x <= 7.5e-229)
		tmp = t_1;
	elseif (x <= 72000000000.0)
		tmp = t_2;
	elseif (x <= 9.5e+85)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+45], t$95$3, If[LessEqual[x, -4.6e-302], t$95$2, If[LessEqual[x, 7.5e-229], t$95$1, If[LessEqual[x, 72000000000.0], t$95$2, If[LessEqual[x, 9.5e+85], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.19999999999999975e45 or 9.49999999999999945e85 < x

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.19999999999999975e45 < x < -4.60000000000000004e-302 or 7.4999999999999999e-229 < x < 7.2e10

   1. Initial program 70.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.60000000000000004e-302 < x < 7.4999999999999999e-229 or 7.2e10 < x < 9.49999999999999945e85

   1. Initial program 75.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 43.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.75 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.24 \cdot 10^{-79}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-195}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-246}:\\ \;\;\;\;-b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 2300000000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* j c) (* x t)))))
   (if (<= a -3.75e-31)
     t_1
     (if (<= a -1.24e-79)
       (* t (* i b))
       (if (<= a -1.8e-195)
         (* x (* y z))
         (if (<= a 6.2e-246)
           (- (* b (* z c)))
           (if (<= a 2300000000000.0) (* y (* x 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 t_1 = a * ((j * c) - (x * t));
	double tmp;
	if (a <= -3.75e-31) {
		tmp = t_1;
	} else if (a <= -1.24e-79) {
		tmp = t * (i * b);
	} else if (a <= -1.8e-195) {
		tmp = x * (y * z);
	} else if (a <= 6.2e-246) {
		tmp = -(b * (z * c));
	} else if (a <= 2300000000000.0) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = a * ((j * c) - (x * t))
    if (a <= (-3.75d-31)) then
        tmp = t_1
    else if (a <= (-1.24d-79)) then
        tmp = t * (i * b)
    else if (a <= (-1.8d-195)) then
        tmp = x * (y * z)
    else if (a <= 6.2d-246) then
        tmp = -(b * (z * c))
    else if (a <= 2300000000000.0d0) then
        tmp = y * (x * 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 t_1 = a * ((j * c) - (x * t));
	double tmp;
	if (a <= -3.75e-31) {
		tmp = t_1;
	} else if (a <= -1.24e-79) {
		tmp = t * (i * b);
	} else if (a <= -1.8e-195) {
		tmp = x * (y * z);
	} else if (a <= 6.2e-246) {
		tmp = -(b * (z * c));
	} else if (a <= 2300000000000.0) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((j * c) - (x * t))
	tmp = 0
	if a <= -3.75e-31:
		tmp = t_1
	elif a <= -1.24e-79:
		tmp = t * (i * b)
	elif a <= -1.8e-195:
		tmp = x * (y * z)
	elif a <= 6.2e-246:
		tmp = -(b * (z * c))
	elif a <= 2300000000000.0:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(j * c) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.75e-31)
		tmp = t_1;
	elseif (a <= -1.24e-79)
		tmp = Float64(t * Float64(i * b));
	elseif (a <= -1.8e-195)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 6.2e-246)
		tmp = Float64(-Float64(b * Float64(z * c)));
	elseif (a <= 2300000000000.0)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((j * c) - (x * t));
	tmp = 0.0;
	if (a <= -3.75e-31)
		tmp = t_1;
	elseif (a <= -1.24e-79)
		tmp = t * (i * b);
	elseif (a <= -1.8e-195)
		tmp = x * (y * z);
	elseif (a <= 6.2e-246)
		tmp = -(b * (z * c));
	elseif (a <= 2300000000000.0)
		tmp = y * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(j * c), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.75e-31], t$95$1, If[LessEqual[a, -1.24e-79], N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.8e-195], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-246], (-N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), If[LessEqual[a, 2300000000000.0], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.74999999999999987e-31 or 2.3e12 < a

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.74999999999999987e-31 < a < -1.24000000000000006e-79

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.24000000000000006e-79 < a < -1.8e-195

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.8e-195 < a < 6.2000000000000001e-246

   1. Initial program 74.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 6.2000000000000001e-246 < a < 2.3e12

   1. Initial program 77.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 14: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(j \cdot \left(c - \frac{i \cdot y}{a}\right)\right)\\ \mathbf{if}\;j \leq -2.75 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+190}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+250}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* j (- c (/ (* i y) a))))))
   (if (<= j -2.75e+97)
     t_1
     (if (<= j 1.85e+26)
       (+ (* x (- (* y z) (* a t))) (* b (- (* t i) (* z c))))
       (if (<= j 2.5e+190)
         (+ (* t (- (* i b) (* x a))) (* j (- (* c a) (* y i))))
         (if (<= j 2.4e+250) (* a (- (* j c) (* x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (j * (c - ((i * y) / a)));
	double tmp;
	if (j <= -2.75e+97) {
		tmp = t_1;
	} else if (j <= 1.85e+26) {
		tmp = (x * ((y * z) - (a * t))) + (b * ((t * i) - (z * c)));
	} else if (j <= 2.5e+190) {
		tmp = (t * ((i * b) - (x * a))) + (j * ((c * a) - (y * i)));
	} else if (j <= 2.4e+250) {
		tmp = a * ((j * c) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = a * (j * (c - ((i * y) / a)))
    if (j <= (-2.75d+97)) then
        tmp = t_1
    else if (j <= 1.85d+26) then
        tmp = (x * ((y * z) - (a * t))) + (b * ((t * i) - (z * c)))
    else if (j <= 2.5d+190) then
        tmp = (t * ((i * b) - (x * a))) + (j * ((c * a) - (y * i)))
    else if (j <= 2.4d+250) then
        tmp = a * ((j * c) - (x * t))
    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 t_1 = a * (j * (c - ((i * y) / a)));
	double tmp;
	if (j <= -2.75e+97) {
		tmp = t_1;
	} else if (j <= 1.85e+26) {
		tmp = (x * ((y * z) - (a * t))) + (b * ((t * i) - (z * c)));
	} else if (j <= 2.5e+190) {
		tmp = (t * ((i * b) - (x * a))) + (j * ((c * a) - (y * i)));
	} else if (j <= 2.4e+250) {
		tmp = a * ((j * c) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (j * (c - ((i * y) / a)))
	tmp = 0
	if j <= -2.75e+97:
		tmp = t_1
	elif j <= 1.85e+26:
		tmp = (x * ((y * z) - (a * t))) + (b * ((t * i) - (z * c)))
	elif j <= 2.5e+190:
		tmp = (t * ((i * b) - (x * a))) + (j * ((c * a) - (y * i)))
	elif j <= 2.4e+250:
		tmp = a * ((j * c) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(j * Float64(c - Float64(Float64(i * y) / a))))
	tmp = 0.0
	if (j <= -2.75e+97)
		tmp = t_1;
	elseif (j <= 1.85e+26)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(a * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (j <= 2.5e+190)
		tmp = Float64(Float64(t * Float64(Float64(i * b) - Float64(x * a))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	elseif (j <= 2.4e+250)
		tmp = Float64(a * Float64(Float64(j * c) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (j * (c - ((i * y) / a)));
	tmp = 0.0;
	if (j <= -2.75e+97)
		tmp = t_1;
	elseif (j <= 1.85e+26)
		tmp = (x * ((y * z) - (a * t))) + (b * ((t * i) - (z * c)));
	elseif (j <= 2.5e+190)
		tmp = (t * ((i * b) - (x * a))) + (j * ((c * a) - (y * i)));
	elseif (j <= 2.4e+250)
		tmp = a * ((j * c) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(j * N[(c - N[(N[(i * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.75e+97], t$95$1, If[LessEqual[j, 1.85e+26], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e+190], N[(N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.4e+250], N[(a * N[(N[(j * c), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.75000000000000011e97 or 2.40000000000000013e250 < j

   1. Initial program 55.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -2.75000000000000011e97 < j < 1.84999999999999994e26

   1. Initial program 77.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.84999999999999994e26 < j < 2.50000000000000018e190

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.50000000000000018e190 < j < 2.40000000000000013e250

   1. Initial program 55.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 15: 30.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -72000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -8.4 \cdot 10^{-288}:\\ \;\;\;\;\left(t \cdot b\right) \cdot i\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (* z c)))))
   (if (<= c -7.5e+58)
     t_1
     (if (<= c -72000000000.0)
       (* x (* y z))
       (if (<= c -8.4e-288)
         (* (* t b) i)
         (if (<= c 2.9e-85)
           (* y (* x z))
           (if (<= c 4.9e+32) (* t (* i 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 t_1 = -(b * (z * c));
	double tmp;
	if (c <= -7.5e+58) {
		tmp = t_1;
	} else if (c <= -72000000000.0) {
		tmp = x * (y * z);
	} else if (c <= -8.4e-288) {
		tmp = (t * b) * i;
	} else if (c <= 2.9e-85) {
		tmp = y * (x * z);
	} else if (c <= 4.9e+32) {
		tmp = t * (i * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = -(b * (z * c))
    if (c <= (-7.5d+58)) then
        tmp = t_1
    else if (c <= (-72000000000.0d0)) then
        tmp = x * (y * z)
    else if (c <= (-8.4d-288)) then
        tmp = (t * b) * i
    else if (c <= 2.9d-85) then
        tmp = y * (x * z)
    else if (c <= 4.9d+32) then
        tmp = t * (i * 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 t_1 = -(b * (z * c));
	double tmp;
	if (c <= -7.5e+58) {
		tmp = t_1;
	} else if (c <= -72000000000.0) {
		tmp = x * (y * z);
	} else if (c <= -8.4e-288) {
		tmp = (t * b) * i;
	} else if (c <= 2.9e-85) {
		tmp = y * (x * z);
	} else if (c <= 4.9e+32) {
		tmp = t * (i * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -(b * (z * c))
	tmp = 0
	if c <= -7.5e+58:
		tmp = t_1
	elif c <= -72000000000.0:
		tmp = x * (y * z)
	elif c <= -8.4e-288:
		tmp = (t * b) * i
	elif c <= 2.9e-85:
		tmp = y * (x * z)
	elif c <= 4.9e+32:
		tmp = t * (i * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(-Float64(b * Float64(z * c)))
	tmp = 0.0
	if (c <= -7.5e+58)
		tmp = t_1;
	elseif (c <= -72000000000.0)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= -8.4e-288)
		tmp = Float64(Float64(t * b) * i);
	elseif (c <= 2.9e-85)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 4.9e+32)
		tmp = Float64(t * Float64(i * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -(b * (z * c));
	tmp = 0.0;
	if (c <= -7.5e+58)
		tmp = t_1;
	elseif (c <= -72000000000.0)
		tmp = x * (y * z);
	elseif (c <= -8.4e-288)
		tmp = (t * b) * i;
	elseif (c <= 2.9e-85)
		tmp = y * (x * z);
	elseif (c <= 4.9e+32)
		tmp = t * (i * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = (-N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[c, -7.5e+58], t$95$1, If[LessEqual[c, -72000000000.0], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.4e-288], N[(N[(t * b), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[c, 2.9e-85], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.9e+32], N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -7.5000000000000001e58 or 4.9000000000000001e32 < c

   1. Initial program 57.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -7.5000000000000001e58 < c < -7.2e10

   1. Initial program 56.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -7.2e10 < c < -8.39999999999999983e-288

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -8.39999999999999983e-288 < c < 2.9000000000000002e-85

   1. Initial program 78.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 2.9000000000000002e-85 < c < 4.9000000000000001e32

   1. Initial program 86.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 16: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{if}\;a \leq -800000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+221}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 10^{+255}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* j c) (* x t)))))
   (if (<= a -800000000.0)
     t_2
     (if (<= a 1.65e+123)
       t_1
       (if (<= a 9.5e+221) t_2 (if (<= a 1e+255) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((j * c) - (x * t));
	double tmp;
	if (a <= -800000000.0) {
		tmp = t_2;
	} else if (a <= 1.65e+123) {
		tmp = t_1;
	} else if (a <= 9.5e+221) {
		tmp = t_2;
	} else if (a <= 1e+255) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((j * c) - (x * t))
    if (a <= (-800000000.0d0)) then
        tmp = t_2
    else if (a <= 1.65d+123) then
        tmp = t_1
    else if (a <= 9.5d+221) then
        tmp = t_2
    else if (a <= 1d+255) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((j * c) - (x * t));
	double tmp;
	if (a <= -800000000.0) {
		tmp = t_2;
	} else if (a <= 1.65e+123) {
		tmp = t_1;
	} else if (a <= 9.5e+221) {
		tmp = t_2;
	} else if (a <= 1e+255) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((j * c) - (x * t))
	tmp = 0
	if a <= -800000000.0:
		tmp = t_2
	elif a <= 1.65e+123:
		tmp = t_1
	elif a <= 9.5e+221:
		tmp = t_2
	elif a <= 1e+255:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(j * c) - Float64(x * t)))
	tmp = 0.0
	if (a <= -800000000.0)
		tmp = t_2;
	elseif (a <= 1.65e+123)
		tmp = t_1;
	elseif (a <= 9.5e+221)
		tmp = t_2;
	elseif (a <= 1e+255)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((j * c) - (x * t));
	tmp = 0.0;
	if (a <= -800000000.0)
		tmp = t_2;
	elseif (a <= 1.65e+123)
		tmp = t_1;
	elseif (a <= 9.5e+221)
		tmp = t_2;
	elseif (a <= 1e+255)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(j * c), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -800000000.0], t$95$2, If[LessEqual[a, 1.65e+123], t$95$1, If[LessEqual[a, 9.5e+221], t$95$2, If[LessEqual[a, 1e+255], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 2 regimes

2. if a < -8e8 or 1.65000000000000001e123 < a < 9.50000000000000044e221 or 9.99999999999999988e254 < a

   1. Initial program 62.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -8e8 < a < 1.65000000000000001e123 or 9.50000000000000044e221 < a < 9.99999999999999988e254

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 31.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := -i \cdot \left(y \cdot j\right)\\ \mathbf{if}\;j \leq -8 \cdot 10^{+250}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (- (* i (* y j)))))
   (if (<= j -8e+250)
     t_2
     (if (<= j -6.2e+148)
       t_1
       (if (<= j -3e+101) t_2 (if (<= j 5.6e+25) (* y (* x 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 t_1 = a * (c * j);
	double t_2 = -(i * (y * j));
	double tmp;
	if (j <= -8e+250) {
		tmp = t_2;
	} else if (j <= -6.2e+148) {
		tmp = t_1;
	} else if (j <= -3e+101) {
		tmp = t_2;
	} else if (j <= 5.6e+25) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = -(i * (y * j))
    if (j <= (-8d+250)) then
        tmp = t_2
    else if (j <= (-6.2d+148)) then
        tmp = t_1
    else if (j <= (-3d+101)) then
        tmp = t_2
    else if (j <= 5.6d+25) then
        tmp = y * (x * 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 t_1 = a * (c * j);
	double t_2 = -(i * (y * j));
	double tmp;
	if (j <= -8e+250) {
		tmp = t_2;
	} else if (j <= -6.2e+148) {
		tmp = t_1;
	} else if (j <= -3e+101) {
		tmp = t_2;
	} else if (j <= 5.6e+25) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = -(i * (y * j))
	tmp = 0
	if j <= -8e+250:
		tmp = t_2
	elif j <= -6.2e+148:
		tmp = t_1
	elif j <= -3e+101:
		tmp = t_2
	elif j <= 5.6e+25:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(-Float64(i * Float64(y * j)))
	tmp = 0.0
	if (j <= -8e+250)
		tmp = t_2;
	elseif (j <= -6.2e+148)
		tmp = t_1;
	elseif (j <= -3e+101)
		tmp = t_2;
	elseif (j <= 5.6e+25)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = -(i * (y * j));
	tmp = 0.0;
	if (j <= -8e+250)
		tmp = t_2;
	elseif (j <= -6.2e+148)
		tmp = t_1;
	elseif (j <= -3e+101)
		tmp = t_2;
	elseif (j <= 5.6e+25)
		tmp = y * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = (-N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[j, -8e+250], t$95$2, If[LessEqual[j, -6.2e+148], t$95$1, If[LessEqual[j, -3e+101], t$95$2, If[LessEqual[j, 5.6e+25], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.9999999999999994e250 or -6.19999999999999951e148 < j < -2.99999999999999993e101

   1. Initial program 62.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -7.9999999999999994e250 < j < -6.19999999999999951e148 or 5.6000000000000003e25 < j

   1. Initial program 56.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -2.99999999999999993e101 < j < 5.6000000000000003e25

   1. Initial program 77.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 29.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.36 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-240}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* i b))))
   (if (<= b -4.8e+32)
     t_1
     (if (<= b -1.36e-297)
       (* y (* x z))
       (if (<= b 3.1e-240)
         (* a (* c j))
         (if (<= b 6.2e-57) (* x (* y 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 t_1 = t * (i * b);
	double tmp;
	if (b <= -4.8e+32) {
		tmp = t_1;
	} else if (b <= -1.36e-297) {
		tmp = y * (x * z);
	} else if (b <= 3.1e-240) {
		tmp = a * (c * j);
	} else if (b <= 6.2e-57) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = t * (i * b)
    if (b <= (-4.8d+32)) then
        tmp = t_1
    else if (b <= (-1.36d-297)) then
        tmp = y * (x * z)
    else if (b <= 3.1d-240) then
        tmp = a * (c * j)
    else if (b <= 6.2d-57) then
        tmp = x * (y * 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 t_1 = t * (i * b);
	double tmp;
	if (b <= -4.8e+32) {
		tmp = t_1;
	} else if (b <= -1.36e-297) {
		tmp = y * (x * z);
	} else if (b <= 3.1e-240) {
		tmp = a * (c * j);
	} else if (b <= 6.2e-57) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (i * b)
	tmp = 0
	if b <= -4.8e+32:
		tmp = t_1
	elif b <= -1.36e-297:
		tmp = y * (x * z)
	elif b <= 3.1e-240:
		tmp = a * (c * j)
	elif b <= 6.2e-57:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(i * b))
	tmp = 0.0
	if (b <= -4.8e+32)
		tmp = t_1;
	elseif (b <= -1.36e-297)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 3.1e-240)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 6.2e-57)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (i * b);
	tmp = 0.0;
	if (b <= -4.8e+32)
		tmp = t_1;
	elseif (b <= -1.36e-297)
		tmp = y * (x * z);
	elseif (b <= 3.1e-240)
		tmp = a * (c * j);
	elseif (b <= 6.2e-57)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+32], t$95$1, If[LessEqual[b, -1.36e-297], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-240], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e-57], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.79999999999999983e32 or 6.19999999999999952e-57 < b

   1. Initial program 73.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -4.79999999999999983e32 < b < -1.36e-297

   1. Initial program 69.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.36e-297 < b < 3.10000000000000017e-240

   1. Initial program 47.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 3.10000000000000017e-240 < b < 6.19999999999999952e-57

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 19: 49.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-95}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1000000000000:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -3.4e+193)
     t_1
     (if (<= b -4.4e-95)
       (* c (- (* a j) (* z b)))
       (if (<= b 1000000000000.0) (* a (- (* j c) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.4e+193) {
		tmp = t_1;
	} else if (b <= -4.4e-95) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 1000000000000.0) {
		tmp = a * ((j * c) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-3.4d+193)) then
        tmp = t_1
    else if (b <= (-4.4d-95)) then
        tmp = c * ((a * j) - (z * b))
    else if (b <= 1000000000000.0d0) then
        tmp = a * ((j * c) - (x * t))
    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 t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.4e+193) {
		tmp = t_1;
	} else if (b <= -4.4e-95) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 1000000000000.0) {
		tmp = a * ((j * c) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.4e+193:
		tmp = t_1
	elif b <= -4.4e-95:
		tmp = c * ((a * j) - (z * b))
	elif b <= 1000000000000.0:
		tmp = a * ((j * c) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.4e+193)
		tmp = t_1;
	elseif (b <= -4.4e-95)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (b <= 1000000000000.0)
		tmp = Float64(a * Float64(Float64(j * c) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.4e+193)
		tmp = t_1;
	elseif (b <= -4.4e-95)
		tmp = c * ((a * j) - (z * b));
	elseif (b <= 1000000000000.0)
		tmp = a * ((j * c) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e+193], t$95$1, If[LessEqual[b, -4.4e-95], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1000000000000.0], N[(a * N[(N[(j * c), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.39999999999999986e193 or 1e12 < b

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.39999999999999986e193 < b < -4.3999999999999998e-95

   1. Initial program 72.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.3999999999999998e-95 < b < 1e12

   1. Initial program 62.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 30.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b\right)\\ \mathbf{if}\;i \leq -1.15 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+28}:\\ \;\;\;\;\left(a \cdot j\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* i b))))
   (if (<= i -1.15e+60)
     t_1
     (if (<= i 1.08e-259)
       (* y (* x z))
       (if (<= i 1.25e+28) (* (* a j) c) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (i * b);
	double tmp;
	if (i <= -1.15e+60) {
		tmp = t_1;
	} else if (i <= 1.08e-259) {
		tmp = y * (x * z);
	} else if (i <= 1.25e+28) {
		tmp = (a * j) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = t * (i * b)
    if (i <= (-1.15d+60)) then
        tmp = t_1
    else if (i <= 1.08d-259) then
        tmp = y * (x * z)
    else if (i <= 1.25d+28) then
        tmp = (a * j) * c
    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 t_1 = t * (i * b);
	double tmp;
	if (i <= -1.15e+60) {
		tmp = t_1;
	} else if (i <= 1.08e-259) {
		tmp = y * (x * z);
	} else if (i <= 1.25e+28) {
		tmp = (a * j) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (i * b)
	tmp = 0
	if i <= -1.15e+60:
		tmp = t_1
	elif i <= 1.08e-259:
		tmp = y * (x * z)
	elif i <= 1.25e+28:
		tmp = (a * j) * c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(i * b))
	tmp = 0.0
	if (i <= -1.15e+60)
		tmp = t_1;
	elseif (i <= 1.08e-259)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 1.25e+28)
		tmp = Float64(Float64(a * j) * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (i * b);
	tmp = 0.0;
	if (i <= -1.15e+60)
		tmp = t_1;
	elseif (i <= 1.08e-259)
		tmp = y * (x * z);
	elseif (i <= 1.25e+28)
		tmp = (a * j) * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.15e+60], t$95$1, If[LessEqual[i, 1.08e-259], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.25e+28], N[(N[(a * j), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.15000000000000008e60 or 1.24999999999999989e28 < i

   1. Initial program 60.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.15000000000000008e60 < i < 1.08000000000000002e-259

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 1.08000000000000002e-259 < i < 1.24999999999999989e28

   1. Initial program 77.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 30.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b\right)\\ \mathbf{if}\;i \leq -4.8 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+34}:\\ \;\;\;\;\left(a \cdot c\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* i b))))
   (if (<= i -4.8e+61)
     t_1
     (if (<= i 1.5e-227)
       (* y (* x z))
       (if (<= i 1.1e+34) (* (* a c) j) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (i * b);
	double tmp;
	if (i <= -4.8e+61) {
		tmp = t_1;
	} else if (i <= 1.5e-227) {
		tmp = y * (x * z);
	} else if (i <= 1.1e+34) {
		tmp = (a * c) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = t * (i * b)
    if (i <= (-4.8d+61)) then
        tmp = t_1
    else if (i <= 1.5d-227) then
        tmp = y * (x * z)
    else if (i <= 1.1d+34) then
        tmp = (a * c) * j
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (i * b);
	double tmp;
	if (i <= -4.8e+61) {
		tmp = t_1;
	} else if (i <= 1.5e-227) {
		tmp = y * (x * z);
	} else if (i <= 1.1e+34) {
		tmp = (a * c) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (i * b)
	tmp = 0
	if i <= -4.8e+61:
		tmp = t_1
	elif i <= 1.5e-227:
		tmp = y * (x * z)
	elif i <= 1.1e+34:
		tmp = (a * c) * j
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(i * b))
	tmp = 0.0
	if (i <= -4.8e+61)
		tmp = t_1;
	elseif (i <= 1.5e-227)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 1.1e+34)
		tmp = Float64(Float64(a * c) * j);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (i * b);
	tmp = 0.0;
	if (i <= -4.8e+61)
		tmp = t_1;
	elseif (i <= 1.5e-227)
		tmp = y * (x * z);
	elseif (i <= 1.1e+34)
		tmp = (a * c) * j;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.8e+61], t$95$1, If[LessEqual[i, 1.5e-227], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.1e+34], N[(N[(a * c), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.7999999999999998e61 or 1.1000000000000001e34 < i

   1. Initial program 60.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -4.7999999999999998e61 < i < 1.5e-227

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 1.5e-227 < i < 1.1000000000000001e34

   1. Initial program 78.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= x -6e-109) t_1 (if (<= x 6.4e+94) (* t (* i 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 t_1 = x * (y * z);
	double tmp;
	if (x <= -6e-109) {
		tmp = t_1;
	} else if (x <= 6.4e+94) {
		tmp = t * (i * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (x <= (-6d-109)) then
        tmp = t_1
    else if (x <= 6.4d+94) then
        tmp = t * (i * 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 t_1 = x * (y * z);
	double tmp;
	if (x <= -6e-109) {
		tmp = t_1;
	} else if (x <= 6.4e+94) {
		tmp = t * (i * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if x <= -6e-109:
		tmp = t_1
	elif x <= 6.4e+94:
		tmp = t * (i * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (x <= -6e-109)
		tmp = t_1;
	elseif (x <= 6.4e+94)
		tmp = Float64(t * Float64(i * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (x <= -6e-109)
		tmp = t_1;
	elseif (x <= 6.4e+94)
		tmp = t * (i * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e-109], t$95$1, If[LessEqual[x, 6.4e+94], N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.00000000000000043e-109 or 6.40000000000000028e94 < x

   1. Initial program 69.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -6.00000000000000043e-109 < x < 6.40000000000000028e94

   1. Initial program 70.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 28.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -3.6 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 140000000:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= j -3.6e+149) t_1 (if (<= j 140000000.0) (* t (* i 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 t_1 = a * (c * j);
	double tmp;
	if (j <= -3.6e+149) {
		tmp = t_1;
	} else if (j <= 140000000.0) {
		tmp = t * (i * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (j <= (-3.6d+149)) then
        tmp = t_1
    else if (j <= 140000000.0d0) then
        tmp = t * (i * 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 t_1 = a * (c * j);
	double tmp;
	if (j <= -3.6e+149) {
		tmp = t_1;
	} else if (j <= 140000000.0) {
		tmp = t * (i * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if j <= -3.6e+149:
		tmp = t_1
	elif j <= 140000000.0:
		tmp = t * (i * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -3.6e+149)
		tmp = t_1;
	elseif (j <= 140000000.0)
		tmp = Float64(t * Float64(i * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (j <= -3.6e+149)
		tmp = t_1;
	elseif (j <= 140000000.0)
		tmp = t * (i * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.6e+149], t$95$1, If[LessEqual[j, 140000000.0], N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -3.59999999999999995e149 or 1.4e8 < j

   1. Initial program 60.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in j around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -3.59999999999999995e149 < j < 1.4e8

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in i around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 22.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.7%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in j around inf 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]
9. Add Preprocessing

Developer target: 59.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))