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

Percentage Accurate: 72.6% → 83.8%

Time: 26.0s

Alternatives: 28

Speedup: 0.5×

• 58.6% 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: 72.6% 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: 83.8% accurate, 0.5× speedup

Math

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

FPCore

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

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(x * Float64(Float64(y * z) - Float64(t * a)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(Float64(Float64(t * b) - Float64(y * j)) - Float64(Float64(z * Float64(Float64(b * c) - Float64(x * y))) / i)));
	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))) + (x * ((y * z) - (t * a)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = i * (((t * b) - (y * j)) - ((z * ((b * c) - (x * y))) / i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(i * N[(N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision] - N[(N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $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 91.7%

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

   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 i around inf 25.9%

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

   5. Simplified 37.0%

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

   6. Taylor expanded in a around 0 61.1%

      \[\leadsto \color{blue}{i \cdot \left(\frac{z \cdot \left(x \cdot y - b \cdot c\right)}{i} - \left(-1 \cdot \left(b \cdot t\right) + j \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.2%

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

Alternative 2: 52.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_4 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.85 \cdot 10^{+64}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-198}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-200}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* b (- (* t i) (* z c))))
        (t_4 (* j (- (* a c) (* y i)))))
   (if (<= j -1.85e+64)
     t_4
     (if (<= j -3.7e-198)
       t_2
       (if (<= j 6.6e-253)
         t_1
         (if (<= j 1.15e-200)
           t_3
           (if (<= j 4.5e-182)
             t_1
             (if (<= j 2.25e-91)
               t_2
               (if (<= j 1.4e-6)
                 t_3
                 (if (<= j 2.1e+32)
                   (* y (- (* x z) (* i j)))
                   (if (<= j 2.6e+113)
                     (* b (* c (- (/ (* t i) c) z)))
                     t_4)))))))))))

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));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = b * ((t * i) - (z * c));
	double t_4 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.85e+64) {
		tmp = t_4;
	} else if (j <= -3.7e-198) {
		tmp = t_2;
	} else if (j <= 6.6e-253) {
		tmp = t_1;
	} else if (j <= 1.15e-200) {
		tmp = t_3;
	} else if (j <= 4.5e-182) {
		tmp = t_1;
	} else if (j <= 2.25e-91) {
		tmp = t_2;
	} else if (j <= 1.4e-6) {
		tmp = t_3;
	} else if (j <= 2.1e+32) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= 2.6e+113) {
		tmp = b * (c * (((t * i) / c) - z));
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = z * ((x * y) - (b * c))
    t_3 = b * ((t * i) - (z * c))
    t_4 = j * ((a * c) - (y * i))
    if (j <= (-1.85d+64)) then
        tmp = t_4
    else if (j <= (-3.7d-198)) then
        tmp = t_2
    else if (j <= 6.6d-253) then
        tmp = t_1
    else if (j <= 1.15d-200) then
        tmp = t_3
    else if (j <= 4.5d-182) then
        tmp = t_1
    else if (j <= 2.25d-91) then
        tmp = t_2
    else if (j <= 1.4d-6) then
        tmp = t_3
    else if (j <= 2.1d+32) then
        tmp = y * ((x * z) - (i * j))
    else if (j <= 2.6d+113) then
        tmp = b * (c * (((t * i) / c) - z))
    else
        tmp = t_4
    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) - (t * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = b * ((t * i) - (z * c));
	double t_4 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.85e+64) {
		tmp = t_4;
	} else if (j <= -3.7e-198) {
		tmp = t_2;
	} else if (j <= 6.6e-253) {
		tmp = t_1;
	} else if (j <= 1.15e-200) {
		tmp = t_3;
	} else if (j <= 4.5e-182) {
		tmp = t_1;
	} else if (j <= 2.25e-91) {
		tmp = t_2;
	} else if (j <= 1.4e-6) {
		tmp = t_3;
	} else if (j <= 2.1e+32) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= 2.6e+113) {
		tmp = b * (c * (((t * i) / c) - z));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = z * ((x * y) - (b * c))
	t_3 = b * ((t * i) - (z * c))
	t_4 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.85e+64:
		tmp = t_4
	elif j <= -3.7e-198:
		tmp = t_2
	elif j <= 6.6e-253:
		tmp = t_1
	elif j <= 1.15e-200:
		tmp = t_3
	elif j <= 4.5e-182:
		tmp = t_1
	elif j <= 2.25e-91:
		tmp = t_2
	elif j <= 1.4e-6:
		tmp = t_3
	elif j <= 2.1e+32:
		tmp = y * ((x * z) - (i * j))
	elif j <= 2.6e+113:
		tmp = b * (c * (((t * i) / c) - z))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_4 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.85e+64)
		tmp = t_4;
	elseif (j <= -3.7e-198)
		tmp = t_2;
	elseif (j <= 6.6e-253)
		tmp = t_1;
	elseif (j <= 1.15e-200)
		tmp = t_3;
	elseif (j <= 4.5e-182)
		tmp = t_1;
	elseif (j <= 2.25e-91)
		tmp = t_2;
	elseif (j <= 1.4e-6)
		tmp = t_3;
	elseif (j <= 2.1e+32)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (j <= 2.6e+113)
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(t * i) / c) - z)));
	else
		tmp = t_4;
	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));
	t_2 = z * ((x * y) - (b * c));
	t_3 = b * ((t * i) - (z * c));
	t_4 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.85e+64)
		tmp = t_4;
	elseif (j <= -3.7e-198)
		tmp = t_2;
	elseif (j <= 6.6e-253)
		tmp = t_1;
	elseif (j <= 1.15e-200)
		tmp = t_3;
	elseif (j <= 4.5e-182)
		tmp = t_1;
	elseif (j <= 2.25e-91)
		tmp = t_2;
	elseif (j <= 1.4e-6)
		tmp = t_3;
	elseif (j <= 2.1e+32)
		tmp = y * ((x * z) - (i * j));
	elseif (j <= 2.6e+113)
		tmp = b * (c * (((t * i) / c) - z));
	else
		tmp = t_4;
	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[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.85e+64], t$95$4, If[LessEqual[j, -3.7e-198], t$95$2, If[LessEqual[j, 6.6e-253], t$95$1, If[LessEqual[j, 1.15e-200], t$95$3, If[LessEqual[j, 4.5e-182], t$95$1, If[LessEqual[j, 2.25e-91], t$95$2, If[LessEqual[j, 1.4e-6], t$95$3, If[LessEqual[j, 2.1e+32], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.6e+113], N[(b * N[(c * N[(N[(N[(t * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.84999999999999992e64 or 2.5999999999999999e113 < j

   1. Initial program 79.1%

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

   3. Taylor expanded in b around 0 83.1%

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

   4. Taylor expanded in j around inf 73.3%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -1.84999999999999992e64 < j < -3.69999999999999971e-198 or 4.4999999999999999e-182 < j < 2.24999999999999988e-91

   1. Initial program 64.3%

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

   3. Taylor expanded in z around inf 59.9%

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

   if -3.69999999999999971e-198 < j < 6.6000000000000002e-253 or 1.15000000000000004e-200 < j < 4.4999999999999999e-182

   1. Initial program 73.3%

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

   3. Taylor expanded in b around 0 62.7%

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

   4. Taylor expanded in j around 0 68.2%

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

   if 6.6000000000000002e-253 < j < 1.15000000000000004e-200 or 2.24999999999999988e-91 < j < 1.39999999999999994e-6

   1. Initial program 66.7%

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

   3. Taylor expanded in b around inf 67.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.2%

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

      2. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   if 1.39999999999999994e-6 < j < 2.1000000000000001e32

   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 y around inf 76.4%

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

      1. +-commutative 76.4%

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

      2. mul-1-neg 76.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 76.4%

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

   5. Simplified 76.4%

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

   if 2.1000000000000001e32 < j < 2.5999999999999999e113

   1. Initial program 64.1%

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

   3. Taylor expanded in b around inf 55.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 55.0%

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

      2. *-commutative 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in c around inf 63.0%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\frac{i \cdot t}{c} - z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.85 \cdot 10^{+64}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-198}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-182}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 29.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+171}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+127}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-27}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-148}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq -6.3 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-262}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-112}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;b \leq 0.000106:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= b -6.4e+171)
     (* i (* t b))
     (if (<= b -4.6e+127)
       (* c (* z (- b)))
       (if (<= b -2.1e+51)
         t_1
         (if (<= b -1.3e-27)
           (* b (* t i))
           (if (<= b -2.5e-148)
             (* i (* y (- j)))
             (if (<= b -6.3e-270)
               (* a (* x (- t)))
               (if (<= b 1.55e-262)
                 (* x (* y z))
                 (if (<= b 7.5e-112)
                   (* j (- (* y i)))
                   (if (<= b 0.000106) t_1 (* z (* b (- c))))))))))))))

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);
	double tmp;
	if (b <= -6.4e+171) {
		tmp = i * (t * b);
	} else if (b <= -4.6e+127) {
		tmp = c * (z * -b);
	} else if (b <= -2.1e+51) {
		tmp = t_1;
	} else if (b <= -1.3e-27) {
		tmp = b * (t * i);
	} else if (b <= -2.5e-148) {
		tmp = i * (y * -j);
	} else if (b <= -6.3e-270) {
		tmp = a * (x * -t);
	} else if (b <= 1.55e-262) {
		tmp = x * (y * z);
	} else if (b <= 7.5e-112) {
		tmp = j * -(y * i);
	} else if (b <= 0.000106) {
		tmp = t_1;
	} else {
		tmp = z * (b * -c);
	}
	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 = z * (x * y)
    if (b <= (-6.4d+171)) then
        tmp = i * (t * b)
    else if (b <= (-4.6d+127)) then
        tmp = c * (z * -b)
    else if (b <= (-2.1d+51)) then
        tmp = t_1
    else if (b <= (-1.3d-27)) then
        tmp = b * (t * i)
    else if (b <= (-2.5d-148)) then
        tmp = i * (y * -j)
    else if (b <= (-6.3d-270)) then
        tmp = a * (x * -t)
    else if (b <= 1.55d-262) then
        tmp = x * (y * z)
    else if (b <= 7.5d-112) then
        tmp = j * -(y * i)
    else if (b <= 0.000106d0) then
        tmp = t_1
    else
        tmp = z * (b * -c)
    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);
	double tmp;
	if (b <= -6.4e+171) {
		tmp = i * (t * b);
	} else if (b <= -4.6e+127) {
		tmp = c * (z * -b);
	} else if (b <= -2.1e+51) {
		tmp = t_1;
	} else if (b <= -1.3e-27) {
		tmp = b * (t * i);
	} else if (b <= -2.5e-148) {
		tmp = i * (y * -j);
	} else if (b <= -6.3e-270) {
		tmp = a * (x * -t);
	} else if (b <= 1.55e-262) {
		tmp = x * (y * z);
	} else if (b <= 7.5e-112) {
		tmp = j * -(y * i);
	} else if (b <= 0.000106) {
		tmp = t_1;
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if b <= -6.4e+171:
		tmp = i * (t * b)
	elif b <= -4.6e+127:
		tmp = c * (z * -b)
	elif b <= -2.1e+51:
		tmp = t_1
	elif b <= -1.3e-27:
		tmp = b * (t * i)
	elif b <= -2.5e-148:
		tmp = i * (y * -j)
	elif b <= -6.3e-270:
		tmp = a * (x * -t)
	elif b <= 1.55e-262:
		tmp = x * (y * z)
	elif b <= 7.5e-112:
		tmp = j * -(y * i)
	elif b <= 0.000106:
		tmp = t_1
	else:
		tmp = z * (b * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (b <= -6.4e+171)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= -4.6e+127)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (b <= -2.1e+51)
		tmp = t_1;
	elseif (b <= -1.3e-27)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= -2.5e-148)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (b <= -6.3e-270)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (b <= 1.55e-262)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 7.5e-112)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (b <= 0.000106)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(b * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (b <= -6.4e+171)
		tmp = i * (t * b);
	elseif (b <= -4.6e+127)
		tmp = c * (z * -b);
	elseif (b <= -2.1e+51)
		tmp = t_1;
	elseif (b <= -1.3e-27)
		tmp = b * (t * i);
	elseif (b <= -2.5e-148)
		tmp = i * (y * -j);
	elseif (b <= -6.3e-270)
		tmp = a * (x * -t);
	elseif (b <= 1.55e-262)
		tmp = x * (y * z);
	elseif (b <= 7.5e-112)
		tmp = j * -(y * i);
	elseif (b <= 0.000106)
		tmp = t_1;
	else
		tmp = z * (b * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.4e+171], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.6e+127], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.1e+51], t$95$1, If[LessEqual[b, -1.3e-27], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.5e-148], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.3e-270], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e-262], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e-112], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 0.000106], t$95$1, N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if b < -6.40000000000000022e171

   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 b around inf 76.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 76.9%

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

      2. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in t around inf 47.6%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.6%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 47.6%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   9. Taylor expanded in b around 0 47.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 47.6%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

       2. associate-*l* 50.8%

          \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot i} \]

       3. *-commutative 50.8%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   11. Simplified 50.8%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   if -6.40000000000000022e171 < b < -4.6000000000000003e127

   1. Initial program 66.5%

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

   3. Taylor expanded in b around inf 68.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 68.3%

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

      2. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in c around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

         \[\leadsto c \cdot \left(\frac{b \cdot \left(i \cdot t\right)}{c} + \color{blue}{\left(-b \cdot z\right)}\right) \]

      3. unsub-neg 67.8%

         \[\leadsto c \cdot \color{blue}{\left(\frac{b \cdot \left(i \cdot t\right)}{c} - b \cdot z\right)} \]

      4. associate-/l* 79.0%

         \[\leadsto c \cdot \left(\color{blue}{b \cdot \frac{i \cdot t}{c}} - b \cdot z\right) \]

      5. associate-/l* 79.0%

         \[\leadsto c \cdot \left(b \cdot \color{blue}{\left(i \cdot \frac{t}{c}\right)} - b \cdot z\right) \]

      6. *-commutative 79.0%

         \[\leadsto c \cdot \left(b \cdot \left(i \cdot \frac{t}{c}\right) - \color{blue}{z \cdot b}\right) \]

   8. Simplified 79.0%

      \[\leadsto \color{blue}{c \cdot \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)} \]

   9. Taylor expanded in i around 0 78.9%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 78.9%

          \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

       2. *-commutative 78.9%

          \[\leadsto c \cdot \left(-\color{blue}{z \cdot b}\right) \]

       3. distribute-rgt-neg-in 78.9%

          \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   11. Simplified 78.9%

       \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   if -4.6000000000000003e127 < b < -2.1000000000000001e51 or 7.5000000000000002e-112 < b < 1.06e-4

   1. Initial program 72.9%

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

   3. Taylor expanded in z around inf 46.6%

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

   4. Taylor expanded in x around inf 39.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 41.7%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   6. Simplified 41.7%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   if -2.1000000000000001e51 < b < -1.30000000000000009e-27

   1. Initial program 89.4%

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

   3. Taylor expanded in b around inf 48.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 48.8%

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

      2. *-commutative 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in t around inf 33.7%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 33.7%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 33.7%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   if -1.30000000000000009e-27 < b < -2.4999999999999999e-148

   1. Initial program 70.8%

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

   3. Taylor expanded in i around inf 40.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 40.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 40.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 40.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 40.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   6. Taylor expanded in y around inf 39.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 39.9%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. mul-1-neg 39.9%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 39.9%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 39.9%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if -2.4999999999999999e-148 < b < -6.30000000000000031e-270

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 70.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 70.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 70.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 70.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 70.5%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 70.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   6. Taylor expanded in c around 0 58.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 58.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 58.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

      3. *-commutative 58.3%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(x \cdot t\right)} \]

   8. Simplified 58.3%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t\right)} \]

   if -6.30000000000000031e-270 < b < 1.5499999999999999e-262

   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 z around inf 58.7%

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

   4. Taylor expanded in x around inf 53.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 1.5499999999999999e-262 < b < 7.5000000000000002e-112

   1. Initial program 59.1%

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

   3. Taylor expanded in i around inf 50.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 50.9%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 50.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 50.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 50.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   6. Taylor expanded in y around inf 50.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 50.9%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. mul-1-neg 50.9%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 50.9%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 50.9%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   9. Taylor expanded in i around 0 50.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 50.9%

          \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

       2. *-commutative 50.9%

          \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

       3. distribute-rgt-neg-in 50.9%

          \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]

       4. associate-*r* 51.0%

          \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]

   11. Simplified 51.0%

       \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]

   if 1.06e-4 < b

   1. Initial program 70.4%

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

   3. Taylor expanded in z around inf 50.6%

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

   4. Taylor expanded in x around 0 35.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 35.7%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. associate-*r* 41.6%

         \[\leadsto -\color{blue}{\left(b \cdot c\right) \cdot z} \]

      3. *-commutative 41.6%

         \[\leadsto -\color{blue}{\left(c \cdot b\right)} \cdot z \]

      4. *-commutative 41.6%

         \[\leadsto -\color{blue}{z \cdot \left(c \cdot b\right)} \]

      5. distribute-rgt-neg-in 41.6%

         \[\leadsto \color{blue}{z \cdot \left(-c \cdot b\right)} \]

      6. distribute-rgt-neg-in 41.6%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   6. Simplified 41.6%

      \[\leadsto \color{blue}{z \cdot \left(c \cdot \left(-b\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+171}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+127}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-27}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-148}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq -6.3 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-262}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-112}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;b \leq 0.000106:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -7.2 \cdot 10^{+109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq -5.1 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(b \cdot \left(i \cdot \frac{t}{c} - z\right)\right)\\ \mathbf{elif}\;j \leq -1.42 \cdot 10^{-198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.95 \cdot 10^{-252}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -7.2e+109)
     t_2
     (if (<= j -7.5e-76)
       (* y (- (* x z) (* i j)))
       (if (<= j -5.1e-132)
         (* c (* b (- (* i (/ t c)) z)))
         (if (<= j -1.42e-198)
           t_1
           (if (<= j 1.95e-252)
             (* x (- (* y z) (* t a)))
             (if (<= j 1.55e-25)
               (* b (- (* t i) (* z c)))
               (if (<= j 1.65e+44)
                 t_1
                 (if (<= j 7.5e+112)
                   (* b (* c (- (/ (* t i) c) z)))
                   t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -7.2e+109) {
		tmp = t_2;
	} else if (j <= -7.5e-76) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= -5.1e-132) {
		tmp = c * (b * ((i * (t / c)) - z));
	} else if (j <= -1.42e-198) {
		tmp = t_1;
	} else if (j <= 1.95e-252) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 1.55e-25) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 1.65e+44) {
		tmp = t_1;
	} else if (j <= 7.5e+112) {
		tmp = b * (c * (((t * i) / c) - z));
	} 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 = z * ((x * y) - (b * c))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-7.2d+109)) then
        tmp = t_2
    else if (j <= (-7.5d-76)) then
        tmp = y * ((x * z) - (i * j))
    else if (j <= (-5.1d-132)) then
        tmp = c * (b * ((i * (t / c)) - z))
    else if (j <= (-1.42d-198)) then
        tmp = t_1
    else if (j <= 1.95d-252) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 1.55d-25) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 1.65d+44) then
        tmp = t_1
    else if (j <= 7.5d+112) then
        tmp = b * (c * (((t * i) / c) - z))
    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 = z * ((x * y) - (b * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -7.2e+109) {
		tmp = t_2;
	} else if (j <= -7.5e-76) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= -5.1e-132) {
		tmp = c * (b * ((i * (t / c)) - z));
	} else if (j <= -1.42e-198) {
		tmp = t_1;
	} else if (j <= 1.95e-252) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 1.55e-25) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 1.65e+44) {
		tmp = t_1;
	} else if (j <= 7.5e+112) {
		tmp = b * (c * (((t * i) / c) - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -7.2e+109:
		tmp = t_2
	elif j <= -7.5e-76:
		tmp = y * ((x * z) - (i * j))
	elif j <= -5.1e-132:
		tmp = c * (b * ((i * (t / c)) - z))
	elif j <= -1.42e-198:
		tmp = t_1
	elif j <= 1.95e-252:
		tmp = x * ((y * z) - (t * a))
	elif j <= 1.55e-25:
		tmp = b * ((t * i) - (z * c))
	elif j <= 1.65e+44:
		tmp = t_1
	elif j <= 7.5e+112:
		tmp = b * (c * (((t * i) / c) - z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -7.2e+109)
		tmp = t_2;
	elseif (j <= -7.5e-76)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (j <= -5.1e-132)
		tmp = Float64(c * Float64(b * Float64(Float64(i * Float64(t / c)) - z)));
	elseif (j <= -1.42e-198)
		tmp = t_1;
	elseif (j <= 1.95e-252)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 1.55e-25)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 1.65e+44)
		tmp = t_1;
	elseif (j <= 7.5e+112)
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(t * i) / c) - z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -7.2e+109)
		tmp = t_2;
	elseif (j <= -7.5e-76)
		tmp = y * ((x * z) - (i * j));
	elseif (j <= -5.1e-132)
		tmp = c * (b * ((i * (t / c)) - z));
	elseif (j <= -1.42e-198)
		tmp = t_1;
	elseif (j <= 1.95e-252)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 1.55e-25)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 1.65e+44)
		tmp = t_1;
	elseif (j <= 7.5e+112)
		tmp = b * (c * (((t * i) / c) - z));
	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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.2e+109], t$95$2, If[LessEqual[j, -7.5e-76], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.1e-132], N[(c * N[(b * N[(N[(i * N[(t / c), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.42e-198], t$95$1, If[LessEqual[j, 1.95e-252], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.55e-25], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.65e+44], t$95$1, If[LessEqual[j, 7.5e+112], N[(b * N[(c * N[(N[(N[(t * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -7.2e109 or 7.5e112 < j

   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 b around 0 82.8%

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

   4. Taylor expanded in j around inf 74.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -7.2e109 < j < -7.4999999999999997e-76

   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 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 67.8%

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

   5. Simplified 67.8%

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

   if -7.4999999999999997e-76 < j < -5.10000000000000005e-132

   1. Initial program 59.6%

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

   3. Taylor expanded in b around inf 42.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 42.8%

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

      2. *-commutative 42.8%

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

   5. Simplified 42.8%

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

   6. Taylor expanded in c around inf 51.6%

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

      1. +-commutative 51.6%

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

      2. mul-1-neg 51.6%

         \[\leadsto c \cdot \left(\frac{b \cdot \left(i \cdot t\right)}{c} + \color{blue}{\left(-b \cdot z\right)}\right) \]

      3. unsub-neg 51.6%

         \[\leadsto c \cdot \color{blue}{\left(\frac{b \cdot \left(i \cdot t\right)}{c} - b \cdot z\right)} \]

      4. associate-/l* 51.4%

         \[\leadsto c \cdot \left(\color{blue}{b \cdot \frac{i \cdot t}{c}} - b \cdot z\right) \]

      5. associate-/l* 54.8%

         \[\leadsto c \cdot \left(b \cdot \color{blue}{\left(i \cdot \frac{t}{c}\right)} - b \cdot z\right) \]

      6. *-commutative 54.8%

         \[\leadsto c \cdot \left(b \cdot \left(i \cdot \frac{t}{c}\right) - \color{blue}{z \cdot b}\right) \]

   8. Simplified 54.8%

      \[\leadsto \color{blue}{c \cdot \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)} \]

   9. Taylor expanded in b around 0 51.4%

      \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(\frac{i \cdot t}{c} - z\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r/ 54.8%

          \[\leadsto c \cdot \left(b \cdot \left(\color{blue}{i \cdot \frac{t}{c}} - z\right)\right) \]

   11. Simplified 54.8%

       \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(i \cdot \frac{t}{c} - z\right)\right)} \]

   if -5.10000000000000005e-132 < j < -1.42000000000000001e-198 or 1.54999999999999997e-25 < j < 1.65000000000000007e44

   1. Initial program 72.1%

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

   3. Taylor expanded in z around inf 66.5%

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

   if -1.42000000000000001e-198 < j < 1.9499999999999999e-252

   1. Initial program 73.9%

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

   3. Taylor expanded in b around 0 62.4%

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

   4. Taylor expanded in j around 0 65.4%

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

   if 1.9499999999999999e-252 < j < 1.54999999999999997e-25

   1. Initial program 67.5%

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

   3. Taylor expanded in b around inf 59.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 59.2%

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

      2. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   if 1.65000000000000007e44 < j < 7.5e112

   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 b around inf 57.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 57.6%

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

      2. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in c around inf 62.3%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\frac{i \cdot t}{c} - z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.2 \cdot 10^{+109}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq -5.1 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(b \cdot \left(i \cdot \frac{t}{c} - z\right)\right)\\ \mathbf{elif}\;j \leq -1.42 \cdot 10^{-198}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.95 \cdot 10^{-252}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.4 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-131}:\\ \;\;\;\;c \cdot \left(b \cdot \left(i \cdot \frac{t}{c} - z\right)\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-293}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(t \cdot \left(b - a \cdot \frac{x}{i}\right)\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -3.4e+107)
     t_1
     (if (<= j -3.7e-76)
       (* y (- (* x z) (* i j)))
       (if (<= j -1.65e-131)
         (* c (* b (- (* i (/ t c)) z)))
         (if (<= j -1.8e-293)
           (* z (- (* x y) (* b c)))
           (if (<= j 5.2e-255)
             (* i (* t (- b (* a (/ x i)))))
             (if (<= j 1.48e+113) (* b (* c (- (/ (* t i) c) 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.4e+107) {
		tmp = t_1;
	} else if (j <= -3.7e-76) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= -1.65e-131) {
		tmp = c * (b * ((i * (t / c)) - z));
	} else if (j <= -1.8e-293) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 5.2e-255) {
		tmp = i * (t * (b - (a * (x / i))));
	} else if (j <= 1.48e+113) {
		tmp = b * (c * (((t * i) / c) - 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 = j * ((a * c) - (y * i))
    if (j <= (-3.4d+107)) then
        tmp = t_1
    else if (j <= (-3.7d-76)) then
        tmp = y * ((x * z) - (i * j))
    else if (j <= (-1.65d-131)) then
        tmp = c * (b * ((i * (t / c)) - z))
    else if (j <= (-1.8d-293)) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 5.2d-255) then
        tmp = i * (t * (b - (a * (x / i))))
    else if (j <= 1.48d+113) then
        tmp = b * (c * (((t * i) / c) - 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.4e+107) {
		tmp = t_1;
	} else if (j <= -3.7e-76) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= -1.65e-131) {
		tmp = c * (b * ((i * (t / c)) - z));
	} else if (j <= -1.8e-293) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 5.2e-255) {
		tmp = i * (t * (b - (a * (x / i))));
	} else if (j <= 1.48e+113) {
		tmp = b * (c * (((t * i) / c) - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -3.4e+107:
		tmp = t_1
	elif j <= -3.7e-76:
		tmp = y * ((x * z) - (i * j))
	elif j <= -1.65e-131:
		tmp = c * (b * ((i * (t / c)) - z))
	elif j <= -1.8e-293:
		tmp = z * ((x * y) - (b * c))
	elif j <= 5.2e-255:
		tmp = i * (t * (b - (a * (x / i))))
	elif j <= 1.48e+113:
		tmp = b * (c * (((t * i) / c) - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.4e+107)
		tmp = t_1;
	elseif (j <= -3.7e-76)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (j <= -1.65e-131)
		tmp = Float64(c * Float64(b * Float64(Float64(i * Float64(t / c)) - z)));
	elseif (j <= -1.8e-293)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 5.2e-255)
		tmp = Float64(i * Float64(t * Float64(b - Float64(a * Float64(x / i)))));
	elseif (j <= 1.48e+113)
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(t * i) / c) - 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 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.4e+107)
		tmp = t_1;
	elseif (j <= -3.7e-76)
		tmp = y * ((x * z) - (i * j));
	elseif (j <= -1.65e-131)
		tmp = c * (b * ((i * (t / c)) - z));
	elseif (j <= -1.8e-293)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 5.2e-255)
		tmp = i * (t * (b - (a * (x / i))));
	elseif (j <= 1.48e+113)
		tmp = b * (c * (((t * i) / c) - 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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.4e+107], t$95$1, If[LessEqual[j, -3.7e-76], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.65e-131], N[(c * N[(b * N[(N[(i * N[(t / c), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.8e-293], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.2e-255], N[(i * N[(t * N[(b - N[(a * N[(x / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.48e+113], N[(b * N[(c * N[(N[(N[(t * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -3.3999999999999997e107 or 1.48000000000000002e113 < j

   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 b around 0 82.8%

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

   4. Taylor expanded in j around inf 74.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -3.3999999999999997e107 < j < -3.70000000000000011e-76

   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 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 67.8%

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

   5. Simplified 67.8%

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

   if -3.70000000000000011e-76 < j < -1.6500000000000001e-131

   1. Initial program 59.6%

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

   3. Taylor expanded in b around inf 42.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 42.8%

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

      2. *-commutative 42.8%

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

   5. Simplified 42.8%

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

   6. Taylor expanded in c around inf 51.6%

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

      1. +-commutative 51.6%

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

      2. mul-1-neg 51.6%

         \[\leadsto c \cdot \left(\frac{b \cdot \left(i \cdot t\right)}{c} + \color{blue}{\left(-b \cdot z\right)}\right) \]

      3. unsub-neg 51.6%

         \[\leadsto c \cdot \color{blue}{\left(\frac{b \cdot \left(i \cdot t\right)}{c} - b \cdot z\right)} \]

      4. associate-/l* 51.4%

         \[\leadsto c \cdot \left(\color{blue}{b \cdot \frac{i \cdot t}{c}} - b \cdot z\right) \]

      5. associate-/l* 54.8%

         \[\leadsto c \cdot \left(b \cdot \color{blue}{\left(i \cdot \frac{t}{c}\right)} - b \cdot z\right) \]

      6. *-commutative 54.8%

         \[\leadsto c \cdot \left(b \cdot \left(i \cdot \frac{t}{c}\right) - \color{blue}{z \cdot b}\right) \]

   8. Simplified 54.8%

      \[\leadsto \color{blue}{c \cdot \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)} \]

   9. Taylor expanded in b around 0 51.4%

      \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(\frac{i \cdot t}{c} - z\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r/ 54.8%

          \[\leadsto c \cdot \left(b \cdot \left(\color{blue}{i \cdot \frac{t}{c}} - z\right)\right) \]

   11. Simplified 54.8%

       \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(i \cdot \frac{t}{c} - z\right)\right)} \]

   if -1.6500000000000001e-131 < j < -1.79999999999999993e-293

   1. Initial program 64.4%

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

   3. Taylor expanded in z around inf 64.0%

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

   if -1.79999999999999993e-293 < j < 5.20000000000000041e-255

   1. Initial program 78.9%

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

   3. Taylor expanded in i around inf 99.7%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in t around inf 75.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(-1 \cdot b + \frac{a \cdot x}{i}\right)\right)\right)} \]

   8. Simplified 75.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(b - a \cdot \frac{x}{i}\right)\right)} \]

   if 5.20000000000000041e-255 < j < 1.48000000000000002e113

   1. Initial program 68.8%

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

   3. Taylor expanded in b around inf 54.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 54.2%

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

      2. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in c around inf 54.4%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\frac{i \cdot t}{c} - z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.4 \cdot 10^{+107}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-131}:\\ \;\;\;\;c \cdot \left(b \cdot \left(i \cdot \frac{t}{c} - z\right)\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-293}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(t \cdot \left(b - a \cdot \frac{x}{i}\right)\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.25 \cdot 10^{+109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-290}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -1.25e+109)
     t_2
     (if (<= j -5.5e-74)
       (* y (- (* x z) (* i j)))
       (if (<= j -1.85e-133)
         t_1
         (if (<= j -1.55e-290)
           (* z (- (* x y) (* b c)))
           (if (<= j 3.3e-229)
             t_1
             (if (<= j 2.4e+113) (* b (* c (- (/ (* t i) c) z))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.25e+109) {
		tmp = t_2;
	} else if (j <= -5.5e-74) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= -1.85e-133) {
		tmp = t_1;
	} else if (j <= -1.55e-290) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 3.3e-229) {
		tmp = t_1;
	} else if (j <= 2.4e+113) {
		tmp = b * (c * (((t * i) / c) - z));
	} 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 * ((b * i) - (x * a))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-1.25d+109)) then
        tmp = t_2
    else if (j <= (-5.5d-74)) then
        tmp = y * ((x * z) - (i * j))
    else if (j <= (-1.85d-133)) then
        tmp = t_1
    else if (j <= (-1.55d-290)) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 3.3d-229) then
        tmp = t_1
    else if (j <= 2.4d+113) then
        tmp = b * (c * (((t * i) / c) - z))
    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 * ((b * i) - (x * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.25e+109) {
		tmp = t_2;
	} else if (j <= -5.5e-74) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= -1.85e-133) {
		tmp = t_1;
	} else if (j <= -1.55e-290) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 3.3e-229) {
		tmp = t_1;
	} else if (j <= 2.4e+113) {
		tmp = b * (c * (((t * i) / c) - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.25e+109:
		tmp = t_2
	elif j <= -5.5e-74:
		tmp = y * ((x * z) - (i * j))
	elif j <= -1.85e-133:
		tmp = t_1
	elif j <= -1.55e-290:
		tmp = z * ((x * y) - (b * c))
	elif j <= 3.3e-229:
		tmp = t_1
	elif j <= 2.4e+113:
		tmp = b * (c * (((t * i) / c) - z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.25e+109)
		tmp = t_2;
	elseif (j <= -5.5e-74)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (j <= -1.85e-133)
		tmp = t_1;
	elseif (j <= -1.55e-290)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 3.3e-229)
		tmp = t_1;
	elseif (j <= 2.4e+113)
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(t * i) / c) - z)));
	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 * ((b * i) - (x * a));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.25e+109)
		tmp = t_2;
	elseif (j <= -5.5e-74)
		tmp = y * ((x * z) - (i * j));
	elseif (j <= -1.85e-133)
		tmp = t_1;
	elseif (j <= -1.55e-290)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 3.3e-229)
		tmp = t_1;
	elseif (j <= 2.4e+113)
		tmp = b * (c * (((t * i) / c) - z));
	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[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.25e+109], t$95$2, If[LessEqual[j, -5.5e-74], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.85e-133], t$95$1, If[LessEqual[j, -1.55e-290], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.3e-229], t$95$1, If[LessEqual[j, 2.4e+113], N[(b * N[(c * N[(N[(N[(t * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.25e109 or 2.39999999999999983e113 < j

   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 b around 0 82.8%

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

   4. Taylor expanded in j around inf 74.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -1.25e109 < j < -5.5000000000000001e-74

   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 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 67.8%

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

   5. Simplified 67.8%

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

   if -5.5000000000000001e-74 < j < -1.85000000000000018e-133 or -1.54999999999999995e-290 < j < 3.30000000000000021e-229

   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 t around inf 64.6%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 64.6%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 64.6%

         \[\leadsto t \cdot \left(-1 \cdot \left(\color{blue}{x \cdot a} - b \cdot i\right)\right) \]

   5. Simplified 64.6%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(x \cdot a - b \cdot i\right)\right)} \]

   if -1.85000000000000018e-133 < j < -1.54999999999999995e-290

   1. Initial program 66.3%

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

   3. Taylor expanded in z around inf 66.0%

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

   if 3.30000000000000021e-229 < j < 2.39999999999999983e113

   1. Initial program 67.7%

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

   3. Taylor expanded in b around inf 52.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 52.5%

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

      2. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in c around inf 52.7%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\frac{i \cdot t}{c} - z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.25 \cdot 10^{+109}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-133}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-290}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-229}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.2 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{-135}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq -2.25 \cdot 10^{-294}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{-229}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -2.2e+107)
     t_1
     (if (<= j -4.2e-74)
       (* y (- (* x z) (* i j)))
       (if (<= j -3e-135)
         (- (* b (* t i)) (* a (* x t)))
         (if (<= j -2.25e-294)
           (* z (- (* x y) (* b c)))
           (if (<= j 6.3e-229)
             (* t (- (* b i) (* x a)))
             (if (<= j 1.48e+113) (* b (* c (- (/ (* t i) c) 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.2e+107) {
		tmp = t_1;
	} else if (j <= -4.2e-74) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= -3e-135) {
		tmp = (b * (t * i)) - (a * (x * t));
	} else if (j <= -2.25e-294) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 6.3e-229) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 1.48e+113) {
		tmp = b * (c * (((t * i) / c) - 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 = j * ((a * c) - (y * i))
    if (j <= (-2.2d+107)) then
        tmp = t_1
    else if (j <= (-4.2d-74)) then
        tmp = y * ((x * z) - (i * j))
    else if (j <= (-3d-135)) then
        tmp = (b * (t * i)) - (a * (x * t))
    else if (j <= (-2.25d-294)) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 6.3d-229) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 1.48d+113) then
        tmp = b * (c * (((t * i) / c) - 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.2e+107) {
		tmp = t_1;
	} else if (j <= -4.2e-74) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= -3e-135) {
		tmp = (b * (t * i)) - (a * (x * t));
	} else if (j <= -2.25e-294) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 6.3e-229) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 1.48e+113) {
		tmp = b * (c * (((t * i) / c) - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.2e+107:
		tmp = t_1
	elif j <= -4.2e-74:
		tmp = y * ((x * z) - (i * j))
	elif j <= -3e-135:
		tmp = (b * (t * i)) - (a * (x * t))
	elif j <= -2.25e-294:
		tmp = z * ((x * y) - (b * c))
	elif j <= 6.3e-229:
		tmp = t * ((b * i) - (x * a))
	elif j <= 1.48e+113:
		tmp = b * (c * (((t * i) / c) - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.2e+107)
		tmp = t_1;
	elseif (j <= -4.2e-74)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (j <= -3e-135)
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(a * Float64(x * t)));
	elseif (j <= -2.25e-294)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 6.3e-229)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 1.48e+113)
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(t * i) / c) - 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 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.2e+107)
		tmp = t_1;
	elseif (j <= -4.2e-74)
		tmp = y * ((x * z) - (i * j));
	elseif (j <= -3e-135)
		tmp = (b * (t * i)) - (a * (x * t));
	elseif (j <= -2.25e-294)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 6.3e-229)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 1.48e+113)
		tmp = b * (c * (((t * i) / c) - 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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.2e+107], t$95$1, If[LessEqual[j, -4.2e-74], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3e-135], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.25e-294], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.3e-229], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.48e+113], N[(b * N[(c * N[(N[(N[(t * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.2e107 or 1.48000000000000002e113 < j

   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 b around 0 82.8%

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

   4. Taylor expanded in j around inf 74.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -2.2e107 < j < -4.2e-74

   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 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 67.8%

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

   5. Simplified 67.8%

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

   if -4.2e-74 < j < -3.00000000000000012e-135

   1. Initial program 55.4%

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

   3. Taylor expanded in j around 0 55.1%

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

   4. Taylor expanded in z around 0 55.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 55.4%

         \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right) - b \cdot \left(i \cdot t\right)\right)} \]

      2. *-commutative 55.4%

         \[\leadsto -1 \cdot \left(a \cdot \color{blue}{\left(x \cdot t\right)} - b \cdot \left(i \cdot t\right)\right) \]

      3. *-commutative 55.4%

         \[\leadsto -1 \cdot \left(a \cdot \left(x \cdot t\right) - b \cdot \color{blue}{\left(t \cdot i\right)}\right) \]

   6. Simplified 55.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot t\right) - b \cdot \left(t \cdot i\right)\right)} \]

   if -3.00000000000000012e-135 < j < -2.24999999999999991e-294

   1. Initial program 66.3%

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

   3. Taylor expanded in z around inf 66.0%

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

   if -2.24999999999999991e-294 < j < 6.29999999999999987e-229

   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 t around inf 72.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 72.3%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 72.3%

         \[\leadsto t \cdot \left(-1 \cdot \left(\color{blue}{x \cdot a} - b \cdot i\right)\right) \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(x \cdot a - b \cdot i\right)\right)} \]

   if 6.29999999999999987e-229 < j < 1.48000000000000002e113

   1. Initial program 67.7%

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

   3. Taylor expanded in b around inf 52.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 52.5%

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

      2. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in c around inf 52.7%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\frac{i \cdot t}{c} - z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.2 \cdot 10^{+107}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{-135}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq -2.25 \cdot 10^{-294}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{-229}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-19}:\\ \;\;\;\;i \cdot \left(\left(t \cdot b - y \cdot j\right) - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{i}\right)\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{-5}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.9e+145)
   (* b (* c (- (/ (* t i) c) z)))
   (if (<= b -1.05e-19)
     (* i (- (- (* t b) (* y j)) (/ (* z (- (* b c) (* x y))) i)))
     (if (<= b 5.7e-5)
       (+
        (- (* x (- (* y z) (* t a))) (* z (* b c)))
        (* j (- (* a c) (* y i))))
       (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.9e+145) {
		tmp = b * (c * (((t * i) / c) - z));
	} else if (b <= -1.05e-19) {
		tmp = i * (((t * b) - (y * j)) - ((z * ((b * c) - (x * y))) / i));
	} else if (b <= 5.7e-5) {
		tmp = ((x * ((y * z) - (t * a))) - (z * (b * c))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	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) :: tmp
    if (b <= (-1.9d+145)) then
        tmp = b * (c * (((t * i) / c) - z))
    else if (b <= (-1.05d-19)) then
        tmp = i * (((t * b) - (y * j)) - ((z * ((b * c) - (x * y))) / i))
    else if (b <= 5.7d-5) then
        tmp = ((x * ((y * z) - (t * a))) - (z * (b * c))) + (j * ((a * c) - (y * i)))
    else
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    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 tmp;
	if (b <= -1.9e+145) {
		tmp = b * (c * (((t * i) / c) - z));
	} else if (b <= -1.05e-19) {
		tmp = i * (((t * b) - (y * j)) - ((z * ((b * c) - (x * y))) / i));
	} else if (b <= 5.7e-5) {
		tmp = ((x * ((y * z) - (t * a))) - (z * (b * c))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.9e+145:
		tmp = b * (c * (((t * i) / c) - z))
	elif b <= -1.05e-19:
		tmp = i * (((t * b) - (y * j)) - ((z * ((b * c) - (x * y))) / i))
	elif b <= 5.7e-5:
		tmp = ((x * ((y * z) - (t * a))) - (z * (b * c))) + (j * ((a * c) - (y * i)))
	else:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.9e+145)
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(t * i) / c) - z)));
	elseif (b <= -1.05e-19)
		tmp = Float64(i * Float64(Float64(Float64(t * b) - Float64(y * j)) - Float64(Float64(z * Float64(Float64(b * c) - Float64(x * y))) / i)));
	elseif (b <= 5.7e-5)
		tmp = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.9e+145)
		tmp = b * (c * (((t * i) / c) - z));
	elseif (b <= -1.05e-19)
		tmp = i * (((t * b) - (y * j)) - ((z * ((b * c) - (x * y))) / i));
	elseif (b <= 5.7e-5)
		tmp = ((x * ((y * z) - (t * a))) - (z * (b * c))) + (j * ((a * c) - (y * i)));
	else
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.9e+145], N[(b * N[(c * N[(N[(N[(t * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.05e-19], N[(i * N[(N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision] - N[(N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.7e-5], N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.90000000000000006e145

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf 78.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 78.1%

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

      2. *-commutative 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in c around inf 78.1%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\frac{i \cdot t}{c} - z\right)\right)} \]

   if -1.90000000000000006e145 < b < -1.0499999999999999e-19

   1. Initial program 85.4%

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

   3. Taylor expanded in i around inf 68.7%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in a around 0 76.2%

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

   if -1.0499999999999999e-19 < b < 5.7000000000000003e-5

   1. Initial program 70.4%

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

   3. Taylor expanded in c around inf 72.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 72.0%

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

      2. *-commutative 72.0%

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

      3. associate-*l* 77.2%

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

      4. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   if 5.7000000000000003e-5 < b

   1. Initial program 70.8%

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

   3. Taylor expanded in y around 0 71.1%

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

   5. Simplified 72.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-19}:\\ \;\;\;\;i \cdot \left(\left(t \cdot b - y \cdot j\right) - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{i}\right)\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{-5}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+142}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.96 \cdot 10^{+83}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-148}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -8e+142)
     t_3
     (if (<= b -1.96e+83)
       t_2
       (if (<= b -1.95e-28)
         t_1
         (if (<= b -4.8e-148)
           t_2
           (if (<= b -5.9e-270) t_1 (if (<= b 2.5e-7) 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 = a * ((c * j) - (x * t));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -8e+142) {
		tmp = t_3;
	} else if (b <= -1.96e+83) {
		tmp = t_2;
	} else if (b <= -1.95e-28) {
		tmp = t_1;
	} else if (b <= -4.8e-148) {
		tmp = t_2;
	} else if (b <= -5.9e-270) {
		tmp = t_1;
	} else if (b <= 2.5e-7) {
		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 = a * ((c * j) - (x * t))
    t_2 = y * ((x * z) - (i * j))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-8d+142)) then
        tmp = t_3
    else if (b <= (-1.96d+83)) then
        tmp = t_2
    else if (b <= (-1.95d-28)) then
        tmp = t_1
    else if (b <= (-4.8d-148)) then
        tmp = t_2
    else if (b <= (-5.9d-270)) then
        tmp = t_1
    else if (b <= 2.5d-7) 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 = a * ((c * j) - (x * t));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -8e+142) {
		tmp = t_3;
	} else if (b <= -1.96e+83) {
		tmp = t_2;
	} else if (b <= -1.95e-28) {
		tmp = t_1;
	} else if (b <= -4.8e-148) {
		tmp = t_2;
	} else if (b <= -5.9e-270) {
		tmp = t_1;
	} else if (b <= 2.5e-7) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = y * ((x * z) - (i * j))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -8e+142:
		tmp = t_3
	elif b <= -1.96e+83:
		tmp = t_2
	elif b <= -1.95e-28:
		tmp = t_1
	elif b <= -4.8e-148:
		tmp = t_2
	elif b <= -5.9e-270:
		tmp = t_1
	elif b <= 2.5e-7:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -8e+142)
		tmp = t_3;
	elseif (b <= -1.96e+83)
		tmp = t_2;
	elseif (b <= -1.95e-28)
		tmp = t_1;
	elseif (b <= -4.8e-148)
		tmp = t_2;
	elseif (b <= -5.9e-270)
		tmp = t_1;
	elseif (b <= 2.5e-7)
		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 = a * ((c * j) - (x * t));
	t_2 = y * ((x * z) - (i * j));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -8e+142)
		tmp = t_3;
	elseif (b <= -1.96e+83)
		tmp = t_2;
	elseif (b <= -1.95e-28)
		tmp = t_1;
	elseif (b <= -4.8e-148)
		tmp = t_2;
	elseif (b <= -5.9e-270)
		tmp = t_1;
	elseif (b <= 2.5e-7)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+142], t$95$3, If[LessEqual[b, -1.96e+83], t$95$2, If[LessEqual[b, -1.95e-28], t$95$1, If[LessEqual[b, -4.8e-148], t$95$2, If[LessEqual[b, -5.9e-270], t$95$1, If[LessEqual[b, 2.5e-7], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.00000000000000041e142 or 2.49999999999999989e-7 < b

   1. Initial program 69.6%

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

   3. Taylor expanded in b around inf 64.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 64.5%

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

      2. *-commutative 64.5%

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

   5. Simplified 64.5%

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

   if -8.00000000000000041e142 < b < -1.96e83 or -1.94999999999999999e-28 < b < -4.8000000000000002e-148 or -5.9e-270 < b < 2.49999999999999989e-7

   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 y around inf 63.2%

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

      1. +-commutative 63.2%

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

      2. mul-1-neg 63.2%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 63.2%

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

   5. Simplified 63.2%

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

   if -1.96e83 < b < -1.94999999999999999e-28 or -4.8000000000000002e-148 < b < -5.9e-270

   1. Initial program 83.5%

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

   3. Taylor expanded in a around inf 57.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 57.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 57.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 57.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 57.4%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 57.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+142}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.96 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-148}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+215}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-128}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-276}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))) (t_2 (* z (* x y))))
   (if (<= a -2.4e+215)
     (* a (* c j))
     (if (<= a -9.8e+64)
       t_1
       (if (<= a -4.1e-128)
         t_2
         (if (<= a -5.5e-276)
           (* b (* t i))
           (if (<= a 1.75e-126)
             t_2
             (if (<= a 1.75e+58) (* t (* b i)) 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 * (x * -t);
	double t_2 = z * (x * y);
	double tmp;
	if (a <= -2.4e+215) {
		tmp = a * (c * j);
	} else if (a <= -9.8e+64) {
		tmp = t_1;
	} else if (a <= -4.1e-128) {
		tmp = t_2;
	} else if (a <= -5.5e-276) {
		tmp = b * (t * i);
	} else if (a <= 1.75e-126) {
		tmp = t_2;
	} else if (a <= 1.75e+58) {
		tmp = t * (b * i);
	} 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 * (x * -t)
    t_2 = z * (x * y)
    if (a <= (-2.4d+215)) then
        tmp = a * (c * j)
    else if (a <= (-9.8d+64)) then
        tmp = t_1
    else if (a <= (-4.1d-128)) then
        tmp = t_2
    else if (a <= (-5.5d-276)) then
        tmp = b * (t * i)
    else if (a <= 1.75d-126) then
        tmp = t_2
    else if (a <= 1.75d+58) then
        tmp = t * (b * i)
    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 * (x * -t);
	double t_2 = z * (x * y);
	double tmp;
	if (a <= -2.4e+215) {
		tmp = a * (c * j);
	} else if (a <= -9.8e+64) {
		tmp = t_1;
	} else if (a <= -4.1e-128) {
		tmp = t_2;
	} else if (a <= -5.5e-276) {
		tmp = b * (t * i);
	} else if (a <= 1.75e-126) {
		tmp = t_2;
	} else if (a <= 1.75e+58) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	t_2 = z * (x * y)
	tmp = 0
	if a <= -2.4e+215:
		tmp = a * (c * j)
	elif a <= -9.8e+64:
		tmp = t_1
	elif a <= -4.1e-128:
		tmp = t_2
	elif a <= -5.5e-276:
		tmp = b * (t * i)
	elif a <= 1.75e-126:
		tmp = t_2
	elif a <= 1.75e+58:
		tmp = t * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (a <= -2.4e+215)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= -9.8e+64)
		tmp = t_1;
	elseif (a <= -4.1e-128)
		tmp = t_2;
	elseif (a <= -5.5e-276)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 1.75e-126)
		tmp = t_2;
	elseif (a <= 1.75e+58)
		tmp = Float64(t * Float64(b * i));
	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 * (x * -t);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (a <= -2.4e+215)
		tmp = a * (c * j);
	elseif (a <= -9.8e+64)
		tmp = t_1;
	elseif (a <= -4.1e-128)
		tmp = t_2;
	elseif (a <= -5.5e-276)
		tmp = b * (t * i);
	elseif (a <= 1.75e-126)
		tmp = t_2;
	elseif (a <= 1.75e+58)
		tmp = t * (b * i);
	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[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+215], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.8e+64], t$95$1, If[LessEqual[a, -4.1e-128], t$95$2, If[LessEqual[a, -5.5e-276], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e-126], t$95$2, If[LessEqual[a, 1.75e+58], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.4000000000000001e215

   1. Initial program 74.4%

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

   3. Taylor expanded in a around inf 82.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 82.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 82.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 82.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 82.8%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 82.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   6. Taylor expanded in c around inf 65.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -2.4000000000000001e215 < a < -9.8000000000000005e64 or 1.7499999999999999e58 < a

   1. Initial program 64.0%

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

   3. Taylor expanded in a around inf 59.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 59.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 59.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 59.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 59.0%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 59.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   6. Taylor expanded in c around 0 39.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 39.8%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 39.8%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

      3. *-commutative 39.8%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(x \cdot t\right)} \]

   8. Simplified 39.8%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t\right)} \]

   if -9.8000000000000005e64 < a < -4.1e-128 or -5.49999999999999972e-276 < a < 1.75e-126

   1. Initial program 77.2%

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

   3. Taylor expanded in z around inf 56.2%

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

   4. Taylor expanded in x around inf 36.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 37.3%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   6. Simplified 37.3%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   if -4.1e-128 < a < -5.49999999999999972e-276

   1. Initial program 76.7%

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

   3. Taylor expanded in b around inf 67.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in t around inf 44.5%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 44.5%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   if 1.75e-126 < a < 1.7499999999999999e58

   1. Initial program 73.9%

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

   3. Taylor expanded in b around inf 50.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.5%

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

      2. *-commutative 50.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in t around inf 30.5%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 30.5%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 30.5%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   9. Taylor expanded in b around 0 30.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 30.5%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

       2. associate-*l* 33.7%

          \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot i} \]

       3. *-commutative 33.7%

          \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot i \]

       4. associate-*r* 35.8%

          \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   11. Simplified 35.8%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+215}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-128}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-276}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+170}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+127}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-146}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 0.0027:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3.2e+170)
   (* i (* t b))
   (if (<= b -4.6e+127)
     (* c (* z (- b)))
     (if (<= b -3e+29)
       (* z (* x y))
       (if (<= b -5.8e-146)
         (* y (* i (- j)))
         (if (<= b -4.1e-270)
           (* a (* x (- t)))
           (if (<= b 0.0027) (* x (* y z)) (* z (* b (- c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.2e+170) {
		tmp = i * (t * b);
	} else if (b <= -4.6e+127) {
		tmp = c * (z * -b);
	} else if (b <= -3e+29) {
		tmp = z * (x * y);
	} else if (b <= -5.8e-146) {
		tmp = y * (i * -j);
	} else if (b <= -4.1e-270) {
		tmp = a * (x * -t);
	} else if (b <= 0.0027) {
		tmp = x * (y * z);
	} else {
		tmp = z * (b * -c);
	}
	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) :: tmp
    if (b <= (-3.2d+170)) then
        tmp = i * (t * b)
    else if (b <= (-4.6d+127)) then
        tmp = c * (z * -b)
    else if (b <= (-3d+29)) then
        tmp = z * (x * y)
    else if (b <= (-5.8d-146)) then
        tmp = y * (i * -j)
    else if (b <= (-4.1d-270)) then
        tmp = a * (x * -t)
    else if (b <= 0.0027d0) then
        tmp = x * (y * z)
    else
        tmp = z * (b * -c)
    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 tmp;
	if (b <= -3.2e+170) {
		tmp = i * (t * b);
	} else if (b <= -4.6e+127) {
		tmp = c * (z * -b);
	} else if (b <= -3e+29) {
		tmp = z * (x * y);
	} else if (b <= -5.8e-146) {
		tmp = y * (i * -j);
	} else if (b <= -4.1e-270) {
		tmp = a * (x * -t);
	} else if (b <= 0.0027) {
		tmp = x * (y * z);
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3.2e+170:
		tmp = i * (t * b)
	elif b <= -4.6e+127:
		tmp = c * (z * -b)
	elif b <= -3e+29:
		tmp = z * (x * y)
	elif b <= -5.8e-146:
		tmp = y * (i * -j)
	elif b <= -4.1e-270:
		tmp = a * (x * -t)
	elif b <= 0.0027:
		tmp = x * (y * z)
	else:
		tmp = z * (b * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3.2e+170)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= -4.6e+127)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (b <= -3e+29)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= -5.8e-146)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (b <= -4.1e-270)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (b <= 0.0027)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(z * Float64(b * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -3.2e+170)
		tmp = i * (t * b);
	elseif (b <= -4.6e+127)
		tmp = c * (z * -b);
	elseif (b <= -3e+29)
		tmp = z * (x * y);
	elseif (b <= -5.8e-146)
		tmp = y * (i * -j);
	elseif (b <= -4.1e-270)
		tmp = a * (x * -t);
	elseif (b <= 0.0027)
		tmp = x * (y * z);
	else
		tmp = z * (b * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3.2e+170], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.6e+127], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e+29], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.8e-146], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.1e-270], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0027], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -3.19999999999999979e170

   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 b around inf 76.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 76.9%

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

      2. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in t around inf 47.6%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.6%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 47.6%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   9. Taylor expanded in b around 0 47.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 47.6%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

       2. associate-*l* 50.8%

          \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot i} \]

       3. *-commutative 50.8%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   11. Simplified 50.8%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   if -3.19999999999999979e170 < b < -4.6000000000000003e127

   1. Initial program 66.5%

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

   3. Taylor expanded in b around inf 68.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 68.3%

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

      2. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in c around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

         \[\leadsto c \cdot \left(\frac{b \cdot \left(i \cdot t\right)}{c} + \color{blue}{\left(-b \cdot z\right)}\right) \]

      3. unsub-neg 67.8%

         \[\leadsto c \cdot \color{blue}{\left(\frac{b \cdot \left(i \cdot t\right)}{c} - b \cdot z\right)} \]

      4. associate-/l* 79.0%

         \[\leadsto c \cdot \left(\color{blue}{b \cdot \frac{i \cdot t}{c}} - b \cdot z\right) \]

      5. associate-/l* 79.0%

         \[\leadsto c \cdot \left(b \cdot \color{blue}{\left(i \cdot \frac{t}{c}\right)} - b \cdot z\right) \]

      6. *-commutative 79.0%

         \[\leadsto c \cdot \left(b \cdot \left(i \cdot \frac{t}{c}\right) - \color{blue}{z \cdot b}\right) \]

   8. Simplified 79.0%

      \[\leadsto \color{blue}{c \cdot \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)} \]

   9. Taylor expanded in i around 0 78.9%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 78.9%

          \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

       2. *-commutative 78.9%

          \[\leadsto c \cdot \left(-\color{blue}{z \cdot b}\right) \]

       3. distribute-rgt-neg-in 78.9%

          \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   11. Simplified 78.9%

       \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   if -4.6000000000000003e127 < b < -2.9999999999999999e29

   1. Initial program 81.6%

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

   3. Taylor expanded in z around inf 38.9%

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

   4. Taylor expanded in x around inf 27.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 31.4%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   6. Simplified 31.4%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   if -2.9999999999999999e29 < b < -5.80000000000000022e-146

   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 i around inf 39.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 39.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 39.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 39.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 39.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   6. Taylor expanded in y around inf 29.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 29.7%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. mul-1-neg 29.7%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 29.7%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 29.7%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   9. Taylor expanded in i around 0 29.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 29.7%

          \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

       2. associate-*r* 40.9%

          \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

       3. distribute-rgt-neg-in 40.9%

          \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

       4. *-commutative 40.9%

          \[\leadsto \color{blue}{\left(j \cdot i\right)} \cdot \left(-y\right) \]

   11. Simplified 40.9%

       \[\leadsto \color{blue}{\left(j \cdot i\right) \cdot \left(-y\right)} \]

   if -5.80000000000000022e-146 < b < -4.0999999999999996e-270

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 70.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 70.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 70.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 70.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 70.5%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 70.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   6. Taylor expanded in c around 0 58.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 58.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 58.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

      3. *-commutative 58.3%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(x \cdot t\right)} \]

   8. Simplified 58.3%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t\right)} \]

   if -4.0999999999999996e-270 < b < 0.0027000000000000001

   1. Initial program 65.1%

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

   3. Taylor expanded in z around inf 39.7%

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

   4. Taylor expanded in x around inf 39.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 0.0027000000000000001 < b

   1. Initial program 70.4%

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

   3. Taylor expanded in z around inf 50.6%

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

   4. Taylor expanded in x around 0 35.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 35.7%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. associate-*r* 41.6%

         \[\leadsto -\color{blue}{\left(b \cdot c\right) \cdot z} \]

      3. *-commutative 41.6%

         \[\leadsto -\color{blue}{\left(c \cdot b\right)} \cdot z \]

      4. *-commutative 41.6%

         \[\leadsto -\color{blue}{z \cdot \left(c \cdot b\right)} \]

      5. distribute-rgt-neg-in 41.6%

         \[\leadsto \color{blue}{z \cdot \left(-c \cdot b\right)} \]

      6. distribute-rgt-neg-in 41.6%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   6. Simplified 41.6%

      \[\leadsto \color{blue}{z \cdot \left(c \cdot \left(-b\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+170}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+127}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-146}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 0.0027:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-196}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+34}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+111}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= t -5.2e+19)
     t_1
     (if (<= t -4.3e-57)
       (* a (* c j))
       (if (<= t 8.2e-196)
         (* j (- (* y i)))
         (if (<= t 7.4e+34)
           (* c (* z (- b)))
           (if (<= t 8.4e+111)
             (* z (* x y))
             (if (<= t 3.5e+197) (* 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 = b * (t * i);
	double tmp;
	if (t <= -5.2e+19) {
		tmp = t_1;
	} else if (t <= -4.3e-57) {
		tmp = a * (c * j);
	} else if (t <= 8.2e-196) {
		tmp = j * -(y * i);
	} else if (t <= 7.4e+34) {
		tmp = c * (z * -b);
	} else if (t <= 8.4e+111) {
		tmp = z * (x * y);
	} else if (t <= 3.5e+197) {
		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 = b * (t * i)
    if (t <= (-5.2d+19)) then
        tmp = t_1
    else if (t <= (-4.3d-57)) then
        tmp = a * (c * j)
    else if (t <= 8.2d-196) then
        tmp = j * -(y * i)
    else if (t <= 7.4d+34) then
        tmp = c * (z * -b)
    else if (t <= 8.4d+111) then
        tmp = z * (x * y)
    else if (t <= 3.5d+197) 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 = b * (t * i);
	double tmp;
	if (t <= -5.2e+19) {
		tmp = t_1;
	} else if (t <= -4.3e-57) {
		tmp = a * (c * j);
	} else if (t <= 8.2e-196) {
		tmp = j * -(y * i);
	} else if (t <= 7.4e+34) {
		tmp = c * (z * -b);
	} else if (t <= 8.4e+111) {
		tmp = z * (x * y);
	} else if (t <= 3.5e+197) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if t <= -5.2e+19:
		tmp = t_1
	elif t <= -4.3e-57:
		tmp = a * (c * j)
	elif t <= 8.2e-196:
		tmp = j * -(y * i)
	elif t <= 7.4e+34:
		tmp = c * (z * -b)
	elif t <= 8.4e+111:
		tmp = z * (x * y)
	elif t <= 3.5e+197:
		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(b * Float64(t * i))
	tmp = 0.0
	if (t <= -5.2e+19)
		tmp = t_1;
	elseif (t <= -4.3e-57)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 8.2e-196)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (t <= 7.4e+34)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (t <= 8.4e+111)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 3.5e+197)
		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 = b * (t * i);
	tmp = 0.0;
	if (t <= -5.2e+19)
		tmp = t_1;
	elseif (t <= -4.3e-57)
		tmp = a * (c * j);
	elseif (t <= 8.2e-196)
		tmp = j * -(y * i);
	elseif (t <= 7.4e+34)
		tmp = c * (z * -b);
	elseif (t <= 8.4e+111)
		tmp = z * (x * y);
	elseif (t <= 3.5e+197)
		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[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+19], t$95$1, If[LessEqual[t, -4.3e-57], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e-196], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[t, 7.4e+34], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.4e+111], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+197], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.2e19 or 3.49999999999999999e197 < t

   1. Initial program 64.0%

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

   3. Taylor expanded in b around inf 51.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 51.0%

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

      2. *-commutative 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in t around inf 41.1%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 41.1%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   if -5.2e19 < t < -4.30000000000000022e-57

   1. Initial program 64.4%

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

   3. Taylor expanded in a around inf 56.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 56.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 56.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 56.7%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 56.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   6. Taylor expanded in c around inf 41.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -4.30000000000000022e-57 < t < 8.20000000000000043e-196

   1. Initial program 86.0%

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

   3. Taylor expanded in i around inf 40.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 40.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 40.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 40.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 40.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   6. Taylor expanded in y around inf 36.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 36.1%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. mul-1-neg 36.1%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 36.1%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 36.1%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   9. Taylor expanded in i around 0 36.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 36.1%

          \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

       2. *-commutative 36.1%

          \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

       3. distribute-rgt-neg-in 36.1%

          \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]

       4. associate-*r* 38.8%

          \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]

   11. Simplified 38.8%

       \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]

   if 8.20000000000000043e-196 < t < 7.40000000000000017e34

   1. Initial program 78.6%

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

   3. Taylor expanded in b around inf 41.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 41.8%

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

      2. *-commutative 41.8%

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

   5. Simplified 41.8%

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

   6. Taylor expanded in c around inf 35.7%

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

      1. +-commutative 35.7%

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

      2. mul-1-neg 35.7%

         \[\leadsto c \cdot \left(\frac{b \cdot \left(i \cdot t\right)}{c} + \color{blue}{\left(-b \cdot z\right)}\right) \]

      3. unsub-neg 35.7%

         \[\leadsto c \cdot \color{blue}{\left(\frac{b \cdot \left(i \cdot t\right)}{c} - b \cdot z\right)} \]

      4. associate-/l* 37.8%

         \[\leadsto c \cdot \left(\color{blue}{b \cdot \frac{i \cdot t}{c}} - b \cdot z\right) \]

      5. associate-/l* 37.8%

         \[\leadsto c \cdot \left(b \cdot \color{blue}{\left(i \cdot \frac{t}{c}\right)} - b \cdot z\right) \]

      6. *-commutative 37.8%

         \[\leadsto c \cdot \left(b \cdot \left(i \cdot \frac{t}{c}\right) - \color{blue}{z \cdot b}\right) \]

   8. Simplified 37.8%

      \[\leadsto \color{blue}{c \cdot \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)} \]

   9. Taylor expanded in i around 0 31.3%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 31.3%

          \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

       2. *-commutative 31.3%

          \[\leadsto c \cdot \left(-\color{blue}{z \cdot b}\right) \]

       3. distribute-rgt-neg-in 31.3%

          \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   11. Simplified 31.3%

       \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   if 7.40000000000000017e34 < t < 8.3999999999999998e111

   1. Initial program 60.8%

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

   3. Taylor expanded in z around inf 64.4%

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

   4. Taylor expanded in x around inf 34.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 46.5%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   6. Simplified 46.5%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   if 8.3999999999999998e111 < t < 3.49999999999999999e197

   1. Initial program 59.0%

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

   3. Taylor expanded in z around inf 53.3%

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

   4. Taylor expanded in x around inf 47.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-196}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+34}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+111}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) + z \cdot \left(x \cdot y\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.1 \cdot 10^{+109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* b (- (* t i) (* z c))) (* z (* x y))))
        (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -3.1e+109)
     t_2
     (if (<= j -5.8e-198)
       t_1
       (if (<= j 2.6e-253)
         (* x (- (* y z) (* t a)))
         (if (<= j 7.5e+92) 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))) + (z * (x * y));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.1e+109) {
		tmp = t_2;
	} else if (j <= -5.8e-198) {
		tmp = t_1;
	} else if (j <= 2.6e-253) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 7.5e+92) {
		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))) + (z * (x * y))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-3.1d+109)) then
        tmp = t_2
    else if (j <= (-5.8d-198)) then
        tmp = t_1
    else if (j <= 2.6d-253) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 7.5d+92) 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))) + (z * (x * y));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.1e+109) {
		tmp = t_2;
	} else if (j <= -5.8e-198) {
		tmp = t_1;
	} else if (j <= 2.6e-253) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 7.5e+92) {
		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))) + (z * (x * y))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -3.1e+109:
		tmp = t_2
	elif j <= -5.8e-198:
		tmp = t_1
	elif j <= 2.6e-253:
		tmp = x * ((y * z) - (t * a))
	elif j <= 7.5e+92:
		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(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(z * Float64(x * y)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.1e+109)
		tmp = t_2;
	elseif (j <= -5.8e-198)
		tmp = t_1;
	elseif (j <= 2.6e-253)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 7.5e+92)
		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))) + (z * (x * y));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.1e+109)
		tmp = t_2;
	elseif (j <= -5.8e-198)
		tmp = t_1;
	elseif (j <= 2.6e-253)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 7.5e+92)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.1e+109], t$95$2, If[LessEqual[j, -5.8e-198], t$95$1, If[LessEqual[j, 2.6e-253], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e+92], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.09999999999999992e109 or 7.49999999999999946e92 < j

   1. Initial program 77.1%

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

   3. Taylor expanded in b around 0 81.3%

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

   4. Taylor expanded in j around inf 73.2%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -3.09999999999999992e109 < j < -5.80000000000000001e-198 or 2.6e-253 < j < 7.49999999999999946e92

   1. Initial program 68.8%

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

   3. Taylor expanded in j around 0 63.8%

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

   4. Taylor expanded in a around 0 60.2%

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

      1. associate-*r* 62.3%

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

      2. *-commutative 62.3%

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

      3. *-commutative 62.3%

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

   6. Simplified 62.3%

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

   if -5.80000000000000001e-198 < j < 2.6e-253

   1. Initial program 73.9%

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

   3. Taylor expanded in b around 0 62.4%

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

   4. Taylor expanded in j around 0 65.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.1 \cdot 10^{+109}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-198}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+92}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -2.9 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -7.6 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-288}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+92}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= j -2.9e-31)
     t_1
     (if (<= j -7.6e-73)
       (* x (* y z))
       (if (<= j -3.5e-202)
         t_2
         (if (<= j -1.15e-288) (* z (* x y)) (if (<= j 1.6e+92) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -2.9e-31) {
		tmp = t_1;
	} else if (j <= -7.6e-73) {
		tmp = x * (y * z);
	} else if (j <= -3.5e-202) {
		tmp = t_2;
	} else if (j <= -1.15e-288) {
		tmp = z * (x * y);
	} else if (j <= 1.6e+92) {
		tmp = t_2;
	} 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 = j * ((a * c) - (y * i))
    t_2 = b * ((t * i) - (z * c))
    if (j <= (-2.9d-31)) then
        tmp = t_1
    else if (j <= (-7.6d-73)) then
        tmp = x * (y * z)
    else if (j <= (-3.5d-202)) then
        tmp = t_2
    else if (j <= (-1.15d-288)) then
        tmp = z * (x * y)
    else if (j <= 1.6d+92) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -2.9e-31) {
		tmp = t_1;
	} else if (j <= -7.6e-73) {
		tmp = x * (y * z);
	} else if (j <= -3.5e-202) {
		tmp = t_2;
	} else if (j <= -1.15e-288) {
		tmp = z * (x * y);
	} else if (j <= 1.6e+92) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if j <= -2.9e-31:
		tmp = t_1
	elif j <= -7.6e-73:
		tmp = x * (y * z)
	elif j <= -3.5e-202:
		tmp = t_2
	elif j <= -1.15e-288:
		tmp = z * (x * y)
	elif j <= 1.6e+92:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -2.9e-31)
		tmp = t_1;
	elseif (j <= -7.6e-73)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= -3.5e-202)
		tmp = t_2;
	elseif (j <= -1.15e-288)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 1.6e+92)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (j <= -2.9e-31)
		tmp = t_1;
	elseif (j <= -7.6e-73)
		tmp = x * (y * z);
	elseif (j <= -3.5e-202)
		tmp = t_2;
	elseif (j <= -1.15e-288)
		tmp = z * (x * y);
	elseif (j <= 1.6e+92)
		tmp = t_2;
	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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.9e-31], t$95$1, If[LessEqual[j, -7.6e-73], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.5e-202], t$95$2, If[LessEqual[j, -1.15e-288], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.6e+92], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.9000000000000001e-31 or 1.60000000000000013e92 < j

   1. Initial program 77.0%

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

   3. Taylor expanded in b around 0 78.7%

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

   4. Taylor expanded in j around inf 68.2%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -2.9000000000000001e-31 < j < -7.6000000000000005e-73

   1. Initial program 80.9%

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

   3. Taylor expanded in z around inf 71.0%

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

   4. Taylor expanded in x around inf 69.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -7.6000000000000005e-73 < j < -3.4999999999999999e-202 or -1.15e-288 < j < 1.60000000000000013e92

   1. Initial program 67.0%

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

   3. Taylor expanded in b around inf 51.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 51.0%

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

      2. *-commutative 51.0%

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

   5. Simplified 51.0%

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

   if -3.4999999999999999e-202 < j < -1.15e-288

   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 z around inf 63.5%

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

   4. Taylor expanded in x around inf 47.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 53.0%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   6. Simplified 53.0%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{-31}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -7.6 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-202}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-288}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+92}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.1 \cdot 10^{-31}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 8.6 \cdot 10^{-254}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -3.1e-31)
     t_3
     (if (<= j -9e-106)
       t_2
       (if (<= j -1.45e-195)
         t_1
         (if (<= j 8.6e-254) t_2 (if (<= j 4.1e+90) 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 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.1e-31) {
		tmp = t_3;
	} else if (j <= -9e-106) {
		tmp = t_2;
	} else if (j <= -1.45e-195) {
		tmp = t_1;
	} else if (j <= 8.6e-254) {
		tmp = t_2;
	} else if (j <= 4.1e+90) {
		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 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-3.1d-31)) then
        tmp = t_3
    else if (j <= (-9d-106)) then
        tmp = t_2
    else if (j <= (-1.45d-195)) then
        tmp = t_1
    else if (j <= 8.6d-254) then
        tmp = t_2
    else if (j <= 4.1d+90) 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 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.1e-31) {
		tmp = t_3;
	} else if (j <= -9e-106) {
		tmp = t_2;
	} else if (j <= -1.45e-195) {
		tmp = t_1;
	} else if (j <= 8.6e-254) {
		tmp = t_2;
	} else if (j <= 4.1e+90) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -3.1e-31:
		tmp = t_3
	elif j <= -9e-106:
		tmp = t_2
	elif j <= -1.45e-195:
		tmp = t_1
	elif j <= 8.6e-254:
		tmp = t_2
	elif j <= 4.1e+90:
		tmp = t_1
	else:
		tmp = t_3
	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(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.1e-31)
		tmp = t_3;
	elseif (j <= -9e-106)
		tmp = t_2;
	elseif (j <= -1.45e-195)
		tmp = t_1;
	elseif (j <= 8.6e-254)
		tmp = t_2;
	elseif (j <= 4.1e+90)
		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 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.1e-31)
		tmp = t_3;
	elseif (j <= -9e-106)
		tmp = t_2;
	elseif (j <= -1.45e-195)
		tmp = t_1;
	elseif (j <= 8.6e-254)
		tmp = t_2;
	elseif (j <= 4.1e+90)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.1e-31], t$95$3, If[LessEqual[j, -9e-106], t$95$2, If[LessEqual[j, -1.45e-195], t$95$1, If[LessEqual[j, 8.6e-254], t$95$2, If[LessEqual[j, 4.1e+90], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.1e-31 or 4.10000000000000042e90 < j

   1. Initial program 77.0%

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

   3. Taylor expanded in b around 0 78.7%

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

   4. Taylor expanded in j around inf 68.2%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -3.1e-31 < j < -8.99999999999999911e-106 or -1.4500000000000001e-195 < j < 8.5999999999999994e-254

   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 b around 0 60.5%

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

   4. Taylor expanded in j around 0 62.5%

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

   if -8.99999999999999911e-106 < j < -1.4500000000000001e-195 or 8.5999999999999994e-254 < j < 4.10000000000000042e90

   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 b around inf 55.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 55.3%

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

      2. *-commutative 55.3%

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

   5. Simplified 55.3%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i - z \cdot c\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.1 \cdot 10^{-31}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8.6 \cdot 10^{-254}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{+90}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+143}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-20}:\\ \;\;\;\;i \cdot \left(\left(t \cdot b - y \cdot j\right) - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{i}\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-6}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.35e+143)
   (* b (* c (- (/ (* t i) c) z)))
   (if (<= b -9e-20)
     (* i (- (- (* t b) (* y j)) (/ (* z (- (* b c) (* x y))) i)))
     (if (<= b 6.8e-6)
       (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
       (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.35e+143) {
		tmp = b * (c * (((t * i) / c) - z));
	} else if (b <= -9e-20) {
		tmp = i * (((t * b) - (y * j)) - ((z * ((b * c) - (x * y))) / i));
	} else if (b <= 6.8e-6) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	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) :: tmp
    if (b <= (-1.35d+143)) then
        tmp = b * (c * (((t * i) / c) - z))
    else if (b <= (-9d-20)) then
        tmp = i * (((t * b) - (y * j)) - ((z * ((b * c) - (x * y))) / i))
    else if (b <= 6.8d-6) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    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 tmp;
	if (b <= -1.35e+143) {
		tmp = b * (c * (((t * i) / c) - z));
	} else if (b <= -9e-20) {
		tmp = i * (((t * b) - (y * j)) - ((z * ((b * c) - (x * y))) / i));
	} else if (b <= 6.8e-6) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.35e+143:
		tmp = b * (c * (((t * i) / c) - z))
	elif b <= -9e-20:
		tmp = i * (((t * b) - (y * j)) - ((z * ((b * c) - (x * y))) / i))
	elif b <= 6.8e-6:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.35e+143)
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(t * i) / c) - z)));
	elseif (b <= -9e-20)
		tmp = Float64(i * Float64(Float64(Float64(t * b) - Float64(y * j)) - Float64(Float64(z * Float64(Float64(b * c) - Float64(x * y))) / i)));
	elseif (b <= 6.8e-6)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.35e+143)
		tmp = b * (c * (((t * i) / c) - z));
	elseif (b <= -9e-20)
		tmp = i * (((t * b) - (y * j)) - ((z * ((b * c) - (x * y))) / i));
	elseif (b <= 6.8e-6)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.35e+143], N[(b * N[(c * N[(N[(N[(t * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9e-20], N[(i * N[(N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision] - N[(N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e-6], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.3500000000000001e143

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf 78.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 78.1%

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

      2. *-commutative 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in c around inf 78.1%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\frac{i \cdot t}{c} - z\right)\right)} \]

   if -1.3500000000000001e143 < b < -9.0000000000000003e-20

   1. Initial program 85.4%

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

   3. Taylor expanded in i around inf 68.7%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in a around 0 76.2%

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

   if -9.0000000000000003e-20 < b < 6.80000000000000012e-6

   1. Initial program 70.4%

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

   3. Taylor expanded in b around 0 76.2%

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

   if 6.80000000000000012e-6 < b

   1. Initial program 70.8%

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

   3. Taylor expanded in y around 0 71.1%

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

   5. Simplified 72.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+143}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-20}:\\ \;\;\;\;i \cdot \left(\left(t \cdot b - y \cdot j\right) - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{i}\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-6}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+99}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* a (* c j))))
   (if (<= a -7.5e+21)
     t_2
     (if (<= a -5e-128)
       t_1
       (if (<= a -9.5e-277)
         (* b (* t i))
         (if (<= a 6.5e-123) t_1 (if (<= a 2.6e+99) (* t (* b i)) 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 = a * (c * j);
	double tmp;
	if (a <= -7.5e+21) {
		tmp = t_2;
	} else if (a <= -5e-128) {
		tmp = t_1;
	} else if (a <= -9.5e-277) {
		tmp = b * (t * i);
	} else if (a <= 6.5e-123) {
		tmp = t_1;
	} else if (a <= 2.6e+99) {
		tmp = t * (b * i);
	} 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 = a * (c * j)
    if (a <= (-7.5d+21)) then
        tmp = t_2
    else if (a <= (-5d-128)) then
        tmp = t_1
    else if (a <= (-9.5d-277)) then
        tmp = b * (t * i)
    else if (a <= 6.5d-123) then
        tmp = t_1
    else if (a <= 2.6d+99) then
        tmp = t * (b * i)
    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 = a * (c * j);
	double tmp;
	if (a <= -7.5e+21) {
		tmp = t_2;
	} else if (a <= -5e-128) {
		tmp = t_1;
	} else if (a <= -9.5e-277) {
		tmp = b * (t * i);
	} else if (a <= 6.5e-123) {
		tmp = t_1;
	} else if (a <= 2.6e+99) {
		tmp = t * (b * i);
	} 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 = a * (c * j)
	tmp = 0
	if a <= -7.5e+21:
		tmp = t_2
	elif a <= -5e-128:
		tmp = t_1
	elif a <= -9.5e-277:
		tmp = b * (t * i)
	elif a <= 6.5e-123:
		tmp = t_1
	elif a <= 2.6e+99:
		tmp = t * (b * i)
	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(a * Float64(c * j))
	tmp = 0.0
	if (a <= -7.5e+21)
		tmp = t_2;
	elseif (a <= -5e-128)
		tmp = t_1;
	elseif (a <= -9.5e-277)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 6.5e-123)
		tmp = t_1;
	elseif (a <= 2.6e+99)
		tmp = Float64(t * Float64(b * i));
	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 = a * (c * j);
	tmp = 0.0;
	if (a <= -7.5e+21)
		tmp = t_2;
	elseif (a <= -5e-128)
		tmp = t_1;
	elseif (a <= -9.5e-277)
		tmp = b * (t * i);
	elseif (a <= 6.5e-123)
		tmp = t_1;
	elseif (a <= 2.6e+99)
		tmp = t * (b * i);
	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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.5e+21], t$95$2, If[LessEqual[a, -5e-128], t$95$1, If[LessEqual[a, -9.5e-277], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-123], t$95$1, If[LessEqual[a, 2.6e+99], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.5e21 or 2.6e99 < a

   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 a around inf 61.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 61.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 61.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 61.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 61.8%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 61.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   6. Taylor expanded in c around inf 35.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -7.5e21 < a < -5.0000000000000001e-128 or -9.5e-277 < a < 6.49999999999999938e-123

   1. Initial program 77.3%

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

   3. Taylor expanded in z around inf 56.0%

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

   4. Taylor expanded in x around inf 37.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -5.0000000000000001e-128 < a < -9.5e-277

   1. Initial program 76.7%

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

   3. Taylor expanded in b around inf 67.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in t around inf 44.5%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 44.5%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   if 6.49999999999999938e-123 < a < 2.6e99

   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 b around inf 49.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 49.6%

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

      2. *-commutative 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in t around inf 31.7%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 31.7%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 31.7%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   9. Taylor expanded in b around 0 31.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 31.7%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

       2. associate-*l* 32.6%

          \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot i} \]

       3. *-commutative 32.6%

          \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot i \]

       4. associate-*r* 34.5%

          \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   11. Simplified 34.5%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+99}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-128}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-276}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= a -1.25e+121)
     t_1
     (if (<= a -7.4e-128)
       (* y (* x z))
       (if (<= a -3e-276)
         (* b (* t i))
         (if (<= a 1.28e-124)
           (* x (* y z))
           (if (<= a 2.3e+97) (* t (* b i)) 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 (a <= -1.25e+121) {
		tmp = t_1;
	} else if (a <= -7.4e-128) {
		tmp = y * (x * z);
	} else if (a <= -3e-276) {
		tmp = b * (t * i);
	} else if (a <= 1.28e-124) {
		tmp = x * (y * z);
	} else if (a <= 2.3e+97) {
		tmp = t * (b * i);
	} 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 (a <= (-1.25d+121)) then
        tmp = t_1
    else if (a <= (-7.4d-128)) then
        tmp = y * (x * z)
    else if (a <= (-3d-276)) then
        tmp = b * (t * i)
    else if (a <= 1.28d-124) then
        tmp = x * (y * z)
    else if (a <= 2.3d+97) then
        tmp = t * (b * i)
    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 (a <= -1.25e+121) {
		tmp = t_1;
	} else if (a <= -7.4e-128) {
		tmp = y * (x * z);
	} else if (a <= -3e-276) {
		tmp = b * (t * i);
	} else if (a <= 1.28e-124) {
		tmp = x * (y * z);
	} else if (a <= 2.3e+97) {
		tmp = t * (b * i);
	} 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 a <= -1.25e+121:
		tmp = t_1
	elif a <= -7.4e-128:
		tmp = y * (x * z)
	elif a <= -3e-276:
		tmp = b * (t * i)
	elif a <= 1.28e-124:
		tmp = x * (y * z)
	elif a <= 2.3e+97:
		tmp = t * (b * i)
	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 (a <= -1.25e+121)
		tmp = t_1;
	elseif (a <= -7.4e-128)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= -3e-276)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 1.28e-124)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 2.3e+97)
		tmp = Float64(t * Float64(b * i));
	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 (a <= -1.25e+121)
		tmp = t_1;
	elseif (a <= -7.4e-128)
		tmp = y * (x * z);
	elseif (a <= -3e-276)
		tmp = b * (t * i);
	elseif (a <= 1.28e-124)
		tmp = x * (y * z);
	elseif (a <= 2.3e+97)
		tmp = t * (b * i);
	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[a, -1.25e+121], t$95$1, If[LessEqual[a, -7.4e-128], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e-276], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.28e-124], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+97], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.25000000000000002e121 or 2.30000000000000006e97 < a

   1. Initial program 65.4%

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

   3. Taylor expanded in a around inf 70.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 70.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 70.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 70.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 70.0%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 70.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   6. Taylor expanded in c around inf 40.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -1.25000000000000002e121 < a < -7.4e-128

   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 b around 0 56.2%

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

   4. Taylor expanded in y around inf 46.6%

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

      1. +-commutative 46.6%

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

      2. mul-1-neg 46.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 46.6%

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

      4. *-commutative 46.6%

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

   6. Simplified 46.6%

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

   7. Taylor expanded in x around inf 28.4%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 28.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   9. Simplified 28.4%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -7.4e-128 < a < -2.99999999999999988e-276

   1. Initial program 76.7%

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

   3. Taylor expanded in b around inf 67.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in t around inf 44.5%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 44.5%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   if -2.99999999999999988e-276 < a < 1.2799999999999999e-124

   1. Initial program 81.6%

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

   3. Taylor expanded in z around inf 54.2%

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

   4. Taylor expanded in x around inf 39.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 1.2799999999999999e-124 < a < 2.30000000000000006e97

   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 b around inf 49.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 49.6%

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

      2. *-commutative 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in t around inf 31.7%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 31.7%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 31.7%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   9. Taylor expanded in b around 0 31.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 31.7%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

       2. associate-*l* 32.6%

          \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot i} \]

       3. *-commutative 32.6%

          \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot i \]

       4. associate-*r* 34.5%

          \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   11. Simplified 34.5%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+121}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-128}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-276}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* a (* c j))))
   (if (<= a -2.55e+123)
     t_2
     (if (<= a -7.4e-128)
       t_1
       (if (<= a -7e-274)
         (* b (* t i))
         (if (<= a 8.5e-127) t_1 (if (<= a 1.45e+97) (* t (* b i)) 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 = z * (x * y);
	double t_2 = a * (c * j);
	double tmp;
	if (a <= -2.55e+123) {
		tmp = t_2;
	} else if (a <= -7.4e-128) {
		tmp = t_1;
	} else if (a <= -7e-274) {
		tmp = b * (t * i);
	} else if (a <= 8.5e-127) {
		tmp = t_1;
	} else if (a <= 1.45e+97) {
		tmp = t * (b * i);
	} 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 = z * (x * y)
    t_2 = a * (c * j)
    if (a <= (-2.55d+123)) then
        tmp = t_2
    else if (a <= (-7.4d-128)) then
        tmp = t_1
    else if (a <= (-7d-274)) then
        tmp = b * (t * i)
    else if (a <= 8.5d-127) then
        tmp = t_1
    else if (a <= 1.45d+97) then
        tmp = t * (b * i)
    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 = z * (x * y);
	double t_2 = a * (c * j);
	double tmp;
	if (a <= -2.55e+123) {
		tmp = t_2;
	} else if (a <= -7.4e-128) {
		tmp = t_1;
	} else if (a <= -7e-274) {
		tmp = b * (t * i);
	} else if (a <= 8.5e-127) {
		tmp = t_1;
	} else if (a <= 1.45e+97) {
		tmp = t * (b * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = a * (c * j)
	tmp = 0
	if a <= -2.55e+123:
		tmp = t_2
	elif a <= -7.4e-128:
		tmp = t_1
	elif a <= -7e-274:
		tmp = b * (t * i)
	elif a <= 8.5e-127:
		tmp = t_1
	elif a <= 1.45e+97:
		tmp = t * (b * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (a <= -2.55e+123)
		tmp = t_2;
	elseif (a <= -7.4e-128)
		tmp = t_1;
	elseif (a <= -7e-274)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 8.5e-127)
		tmp = t_1;
	elseif (a <= 1.45e+97)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = a * (c * j);
	tmp = 0.0;
	if (a <= -2.55e+123)
		tmp = t_2;
	elseif (a <= -7.4e-128)
		tmp = t_1;
	elseif (a <= -7e-274)
		tmp = b * (t * i);
	elseif (a <= 8.5e-127)
		tmp = t_1;
	elseif (a <= 1.45e+97)
		tmp = t * (b * i);
	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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.55e+123], t$95$2, If[LessEqual[a, -7.4e-128], t$95$1, If[LessEqual[a, -7e-274], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-127], t$95$1, If[LessEqual[a, 1.45e+97], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.54999999999999986e123 or 1.44999999999999994e97 < a

   1. Initial program 65.4%

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

   3. Taylor expanded in a around inf 70.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 70.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 70.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 70.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 70.0%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 70.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   6. Taylor expanded in c around inf 40.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -2.54999999999999986e123 < a < -7.4e-128 or -6.99999999999999963e-274 < a < 8.5e-127

   1. Initial program 76.4%

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

   3. Taylor expanded in z around inf 52.6%

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

   4. Taylor expanded in x around inf 32.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 34.4%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   6. Simplified 34.4%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   if -7.4e-128 < a < -6.99999999999999963e-274

   1. Initial program 76.7%

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

   3. Taylor expanded in b around inf 67.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in t around inf 44.5%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 44.5%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   if 8.5e-127 < a < 1.44999999999999994e97

   1. Initial program 73.0%

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

   3. Taylor expanded in b around inf 48.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 48.6%

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

      2. *-commutative 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in t around inf 31.1%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 31.1%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 31.1%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   9. Taylor expanded in b around 0 31.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 31.1%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

       2. associate-*l* 31.9%

          \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot i} \]

       3. *-commutative 31.9%

          \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot i \]

       4. associate-*r* 33.8%

          \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   11. Simplified 33.8%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-128}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 28.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+35}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= t -8e+17)
     t_1
     (if (<= t -4.2e-97)
       (* a (* c j))
       (if (<= t -3.5e-234)
         (* y (* x z))
         (if (<= t 1.15e+35)
           (* c (* z (- b)))
           (if (<= t 3.5e+197) (* 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 = b * (t * i);
	double tmp;
	if (t <= -8e+17) {
		tmp = t_1;
	} else if (t <= -4.2e-97) {
		tmp = a * (c * j);
	} else if (t <= -3.5e-234) {
		tmp = y * (x * z);
	} else if (t <= 1.15e+35) {
		tmp = c * (z * -b);
	} else if (t <= 3.5e+197) {
		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 = b * (t * i)
    if (t <= (-8d+17)) then
        tmp = t_1
    else if (t <= (-4.2d-97)) then
        tmp = a * (c * j)
    else if (t <= (-3.5d-234)) then
        tmp = y * (x * z)
    else if (t <= 1.15d+35) then
        tmp = c * (z * -b)
    else if (t <= 3.5d+197) 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 = b * (t * i);
	double tmp;
	if (t <= -8e+17) {
		tmp = t_1;
	} else if (t <= -4.2e-97) {
		tmp = a * (c * j);
	} else if (t <= -3.5e-234) {
		tmp = y * (x * z);
	} else if (t <= 1.15e+35) {
		tmp = c * (z * -b);
	} else if (t <= 3.5e+197) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if t <= -8e+17:
		tmp = t_1
	elif t <= -4.2e-97:
		tmp = a * (c * j)
	elif t <= -3.5e-234:
		tmp = y * (x * z)
	elif t <= 1.15e+35:
		tmp = c * (z * -b)
	elif t <= 3.5e+197:
		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(b * Float64(t * i))
	tmp = 0.0
	if (t <= -8e+17)
		tmp = t_1;
	elseif (t <= -4.2e-97)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= -3.5e-234)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 1.15e+35)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (t <= 3.5e+197)
		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 = b * (t * i);
	tmp = 0.0;
	if (t <= -8e+17)
		tmp = t_1;
	elseif (t <= -4.2e-97)
		tmp = a * (c * j);
	elseif (t <= -3.5e-234)
		tmp = y * (x * z);
	elseif (t <= 1.15e+35)
		tmp = c * (z * -b);
	elseif (t <= 3.5e+197)
		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[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+17], t$95$1, If[LessEqual[t, -4.2e-97], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e-234], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+35], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+197], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8e17 or 3.49999999999999999e197 < t

   1. Initial program 64.0%

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

   3. Taylor expanded in b around inf 51.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 51.0%

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

      2. *-commutative 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in t around inf 41.1%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 41.1%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   if -8e17 < t < -4.2000000000000002e-97

   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 a around inf 54.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 54.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 54.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 54.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 54.2%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 54.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   6. Taylor expanded in c around inf 41.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -4.2000000000000002e-97 < t < -3.5000000000000001e-234

   1. Initial program 80.7%

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

   3. Taylor expanded in b around 0 72.1%

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

   4. Taylor expanded in y around inf 59.4%

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

      1. +-commutative 59.4%

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

      2. mul-1-neg 59.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 59.4%

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

      4. *-commutative 59.4%

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

   6. Simplified 59.4%

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

   7. Taylor expanded in x around inf 40.6%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   9. Simplified 40.6%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -3.5000000000000001e-234 < t < 1.1499999999999999e35

   1. Initial program 81.8%

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

   3. Taylor expanded in b around inf 37.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 37.8%

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

      2. *-commutative 37.8%

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

   5. Simplified 37.8%

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

   6. Taylor expanded in c around inf 32.9%

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

      1. +-commutative 32.9%

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

      2. mul-1-neg 32.9%

         \[\leadsto c \cdot \left(\frac{b \cdot \left(i \cdot t\right)}{c} + \color{blue}{\left(-b \cdot z\right)}\right) \]

      3. unsub-neg 32.9%

         \[\leadsto c \cdot \color{blue}{\left(\frac{b \cdot \left(i \cdot t\right)}{c} - b \cdot z\right)} \]

      4. associate-/l* 34.2%

         \[\leadsto c \cdot \left(\color{blue}{b \cdot \frac{i \cdot t}{c}} - b \cdot z\right) \]

      5. associate-/l* 34.2%

         \[\leadsto c \cdot \left(b \cdot \color{blue}{\left(i \cdot \frac{t}{c}\right)} - b \cdot z\right) \]

      6. *-commutative 34.2%

         \[\leadsto c \cdot \left(b \cdot \left(i \cdot \frac{t}{c}\right) - \color{blue}{z \cdot b}\right) \]

   8. Simplified 34.2%

      \[\leadsto \color{blue}{c \cdot \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)} \]

   9. Taylor expanded in i around 0 30.2%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 30.2%

          \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

       2. *-commutative 30.2%

          \[\leadsto c \cdot \left(-\color{blue}{z \cdot b}\right) \]

       3. distribute-rgt-neg-in 30.2%

          \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   11. Simplified 30.2%

       \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   if 1.1499999999999999e35 < t < 3.49999999999999999e197

   1. Initial program 59.9%

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

   3. Taylor expanded in z around inf 58.5%

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

   4. Taylor expanded in x around inf 41.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+35}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-201}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= t -1.6e+20)
     t_1
     (if (<= t -4.5e-57)
       (* a (* c j))
       (if (<= t 7.2e-201)
         (* j (- (* y i)))
         (if (<= t 7e+34)
           (* z (* b (- c)))
           (if (<= t 4e+197) (* 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 = b * (t * i);
	double tmp;
	if (t <= -1.6e+20) {
		tmp = t_1;
	} else if (t <= -4.5e-57) {
		tmp = a * (c * j);
	} else if (t <= 7.2e-201) {
		tmp = j * -(y * i);
	} else if (t <= 7e+34) {
		tmp = z * (b * -c);
	} else if (t <= 4e+197) {
		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 = b * (t * i)
    if (t <= (-1.6d+20)) then
        tmp = t_1
    else if (t <= (-4.5d-57)) then
        tmp = a * (c * j)
    else if (t <= 7.2d-201) then
        tmp = j * -(y * i)
    else if (t <= 7d+34) then
        tmp = z * (b * -c)
    else if (t <= 4d+197) 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 = b * (t * i);
	double tmp;
	if (t <= -1.6e+20) {
		tmp = t_1;
	} else if (t <= -4.5e-57) {
		tmp = a * (c * j);
	} else if (t <= 7.2e-201) {
		tmp = j * -(y * i);
	} else if (t <= 7e+34) {
		tmp = z * (b * -c);
	} else if (t <= 4e+197) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if t <= -1.6e+20:
		tmp = t_1
	elif t <= -4.5e-57:
		tmp = a * (c * j)
	elif t <= 7.2e-201:
		tmp = j * -(y * i)
	elif t <= 7e+34:
		tmp = z * (b * -c)
	elif t <= 4e+197:
		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(b * Float64(t * i))
	tmp = 0.0
	if (t <= -1.6e+20)
		tmp = t_1;
	elseif (t <= -4.5e-57)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 7.2e-201)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (t <= 7e+34)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (t <= 4e+197)
		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 = b * (t * i);
	tmp = 0.0;
	if (t <= -1.6e+20)
		tmp = t_1;
	elseif (t <= -4.5e-57)
		tmp = a * (c * j);
	elseif (t <= 7.2e-201)
		tmp = j * -(y * i);
	elseif (t <= 7e+34)
		tmp = z * (b * -c);
	elseif (t <= 4e+197)
		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[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+20], t$95$1, If[LessEqual[t, -4.5e-57], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-201], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[t, 7e+34], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+197], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.6e20 or 3.9999999999999998e197 < t

   1. Initial program 64.0%

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

   3. Taylor expanded in b around inf 51.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 51.0%

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

      2. *-commutative 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in t around inf 41.1%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 41.1%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   if -1.6e20 < t < -4.49999999999999973e-57

   1. Initial program 64.4%

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

   3. Taylor expanded in a around inf 56.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 56.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 56.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 56.7%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 56.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   6. Taylor expanded in c around inf 41.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -4.49999999999999973e-57 < t < 7.20000000000000063e-201

   1. Initial program 86.0%

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

   3. Taylor expanded in i around inf 40.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 40.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 40.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 40.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 40.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   6. Taylor expanded in y around inf 36.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 36.1%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. mul-1-neg 36.1%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 36.1%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 36.1%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   9. Taylor expanded in i around 0 36.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 36.1%

          \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

       2. *-commutative 36.1%

          \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

       3. distribute-rgt-neg-in 36.1%

          \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]

       4. associate-*r* 38.8%

          \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]

   11. Simplified 38.8%

       \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]

   if 7.20000000000000063e-201 < t < 6.99999999999999996e34

   1. Initial program 78.6%

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

   3. Taylor expanded in z around inf 48.6%

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

   4. Taylor expanded in x around 0 33.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.4%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. associate-*r* 33.3%

         \[\leadsto -\color{blue}{\left(b \cdot c\right) \cdot z} \]

      3. *-commutative 33.3%

         \[\leadsto -\color{blue}{\left(c \cdot b\right)} \cdot z \]

      4. *-commutative 33.3%

         \[\leadsto -\color{blue}{z \cdot \left(c \cdot b\right)} \]

      5. distribute-rgt-neg-in 33.3%

         \[\leadsto \color{blue}{z \cdot \left(-c \cdot b\right)} \]

      6. distribute-rgt-neg-in 33.3%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   6. Simplified 33.3%

      \[\leadsto \color{blue}{z \cdot \left(c \cdot \left(-b\right)\right)} \]

   if 6.99999999999999996e34 < t < 3.9999999999999998e197

   1. Initial program 59.9%

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

   3. Taylor expanded in z around inf 58.5%

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

   4. Taylor expanded in x around inf 41.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+20}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-201}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 52.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+95}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{+57} \lor \neg \left(a \leq 38000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.4e+126)
     t_1
     (if (<= a -2.1e+95)
       (* i (- (* t b) (* y j)))
       (if (or (<= a -1.02e+57) (not (<= a 38000.0)))
         t_1
         (* b (- (* t i) (* z c))))))))

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) - (x * t));
	double tmp;
	if (a <= -1.4e+126) {
		tmp = t_1;
	} else if (a <= -2.1e+95) {
		tmp = i * ((t * b) - (y * j));
	} else if ((a <= -1.02e+57) || !(a <= 38000.0)) {
		tmp = t_1;
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	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) - (x * t))
    if (a <= (-1.4d+126)) then
        tmp = t_1
    else if (a <= (-2.1d+95)) then
        tmp = i * ((t * b) - (y * j))
    else if ((a <= (-1.02d+57)) .or. (.not. (a <= 38000.0d0))) then
        tmp = t_1
    else
        tmp = b * ((t * i) - (z * c))
    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) - (x * t));
	double tmp;
	if (a <= -1.4e+126) {
		tmp = t_1;
	} else if (a <= -2.1e+95) {
		tmp = i * ((t * b) - (y * j));
	} else if ((a <= -1.02e+57) || !(a <= 38000.0)) {
		tmp = t_1;
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.4e+126:
		tmp = t_1
	elif a <= -2.1e+95:
		tmp = i * ((t * b) - (y * j))
	elif (a <= -1.02e+57) or not (a <= 38000.0):
		tmp = t_1
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.4e+126)
		tmp = t_1;
	elseif (a <= -2.1e+95)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif ((a <= -1.02e+57) || !(a <= 38000.0))
		tmp = t_1;
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.4e+126)
		tmp = t_1;
	elseif (a <= -2.1e+95)
		tmp = i * ((t * b) - (y * j));
	elseif ((a <= -1.02e+57) || ~((a <= 38000.0)))
		tmp = t_1;
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+126], t$95$1, If[LessEqual[a, -2.1e+95], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -1.02e+57], N[Not[LessEqual[a, 38000.0]], $MachinePrecision]], t$95$1, N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.40000000000000005e126 or -2.1e95 < a < -1.02e57 or 38000 < a

   1. Initial program 67.0%

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

   3. Taylor expanded in a around inf 66.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 66.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 66.5%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 66.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   if -1.40000000000000005e126 < a < -2.1e95

   1. Initial program 60.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 60.5%

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

      2. fma-define 60.5%

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

      3. *-commutative 60.5%

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

      4. sub-neg 60.5%

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

      5. *-commutative 60.5%

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

      6. sub-neg 60.5%

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

      7. *-commutative 60.5%

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

      8. *-commutative 60.5%

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

   3. Simplified 60.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 41.8%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 41.8%

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

      2. *-commutative 41.8%

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

      3. distribute-rgt-neg-in 41.8%

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

      4. +-commutative 41.8%

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

      5. mul-1-neg 41.8%

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

      6. *-commutative 41.8%

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

      7. unsub-neg 41.8%

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

      8. associate-/l* 41.8%

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

      9. *-commutative 41.8%

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

      10. *-commutative 41.8%

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

      11. *-commutative 41.8%

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

   7. Simplified 41.8%

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

   8. Taylor expanded in i around inf 60.7%

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

      1. +-commutative 60.7%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 60.7%

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

      3. *-commutative 60.7%

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

      4. unsub-neg 60.7%

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

      5. *-commutative 60.7%

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

   10. Simplified 60.7%

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

   if -1.02e57 < a < 38000

   1. Initial program 77.2%

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

   3. Taylor expanded in b around inf 48.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 48.0%

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

      2. *-commutative 48.0%

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

   5. Simplified 48.0%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i - z \cdot c\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+95}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{+57} \lor \neg \left(a \leq 38000\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 42.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.6e-7)
     t_2
     (if (<= a -1.3e-128)
       t_1
       (if (<= a -2.4e-273) (* b (* t i)) (if (<= a 8e-151) 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 = z * (x * y);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.6e-7) {
		tmp = t_2;
	} else if (a <= -1.3e-128) {
		tmp = t_1;
	} else if (a <= -2.4e-273) {
		tmp = b * (t * i);
	} else if (a <= 8e-151) {
		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 = z * (x * y)
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.6d-7)) then
        tmp = t_2
    else if (a <= (-1.3d-128)) then
        tmp = t_1
    else if (a <= (-2.4d-273)) then
        tmp = b * (t * i)
    else if (a <= 8d-151) 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 = z * (x * y);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.6e-7) {
		tmp = t_2;
	} else if (a <= -1.3e-128) {
		tmp = t_1;
	} else if (a <= -2.4e-273) {
		tmp = b * (t * i);
	} else if (a <= 8e-151) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.6e-7:
		tmp = t_2
	elif a <= -1.3e-128:
		tmp = t_1
	elif a <= -2.4e-273:
		tmp = b * (t * i)
	elif a <= 8e-151:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.6e-7)
		tmp = t_2;
	elseif (a <= -1.3e-128)
		tmp = t_1;
	elseif (a <= -2.4e-273)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 8e-151)
		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 = z * (x * y);
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.6e-7)
		tmp = t_2;
	elseif (a <= -1.3e-128)
		tmp = t_1;
	elseif (a <= -2.4e-273)
		tmp = b * (t * i);
	elseif (a <= 8e-151)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e-7], t$95$2, If[LessEqual[a, -1.3e-128], t$95$1, If[LessEqual[a, -2.4e-273], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-151], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6e-7 or 7.9999999999999995e-151 < a

   1. Initial program 69.6%

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

   3. Taylor expanded in a around inf 53.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 53.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 53.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 53.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 53.0%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 53.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   if -1.6e-7 < a < -1.2999999999999999e-128 or -2.39999999999999982e-273 < a < 7.9999999999999995e-151

   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 z around inf 62.1%

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

   4. Taylor expanded in x around inf 41.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 43.3%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   6. Simplified 43.3%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   if -1.2999999999999999e-128 < a < -2.39999999999999982e-273

   1. Initial program 76.7%

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

   3. Taylor expanded in b around inf 67.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in t around inf 44.5%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 44.5%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-7}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-128}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-151}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 52.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-141}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;a \leq 1700000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.05e+56)
     t_2
     (if (<= a 4.9e-178)
       t_1
       (if (<= a 1.75e-141)
         (* j (- (* y i)))
         (if (<= a 1700000000000.0) 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 * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.05e+56) {
		tmp = t_2;
	} else if (a <= 4.9e-178) {
		tmp = t_1;
	} else if (a <= 1.75e-141) {
		tmp = j * -(y * i);
	} else if (a <= 1700000000000.0) {
		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 * ((c * j) - (x * t))
    if (a <= (-1.05d+56)) then
        tmp = t_2
    else if (a <= 4.9d-178) then
        tmp = t_1
    else if (a <= 1.75d-141) then
        tmp = j * -(y * i)
    else if (a <= 1700000000000.0d0) 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 * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.05e+56) {
		tmp = t_2;
	} else if (a <= 4.9e-178) {
		tmp = t_1;
	} else if (a <= 1.75e-141) {
		tmp = j * -(y * i);
	} else if (a <= 1700000000000.0) {
		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 * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.05e+56:
		tmp = t_2
	elif a <= 4.9e-178:
		tmp = t_1
	elif a <= 1.75e-141:
		tmp = j * -(y * i)
	elif a <= 1700000000000.0:
		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(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.05e+56)
		tmp = t_2;
	elseif (a <= 4.9e-178)
		tmp = t_1;
	elseif (a <= 1.75e-141)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (a <= 1700000000000.0)
		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 * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.05e+56)
		tmp = t_2;
	elseif (a <= 4.9e-178)
		tmp = t_1;
	elseif (a <= 1.75e-141)
		tmp = j * -(y * i);
	elseif (a <= 1700000000000.0)
		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[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e+56], t$95$2, If[LessEqual[a, 4.9e-178], t$95$1, If[LessEqual[a, 1.75e-141], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[a, 1700000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.05000000000000009e56 or 1.7e12 < a

   1. Initial program 66.5%

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

   3. Taylor expanded in a around inf 61.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 61.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 61.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 61.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 61.8%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 61.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   if -1.05000000000000009e56 < a < 4.9000000000000002e-178 or 1.7500000000000001e-141 < a < 1.7e12

   1. Initial program 76.6%

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

   3. Taylor expanded in b around inf 50.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.7%

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

      2. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   if 4.9000000000000002e-178 < a < 1.7500000000000001e-141

   1. Initial program 83.3%

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

   3. Taylor expanded in i around inf 48.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 48.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 48.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 48.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 48.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   6. Taylor expanded in y around inf 48.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 48.4%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. mul-1-neg 48.4%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 48.4%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 48.4%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   9. Taylor expanded in i around 0 48.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 48.4%

          \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

       2. *-commutative 48.4%

          \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

       3. distribute-rgt-neg-in 48.4%

          \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]

       4. associate-*r* 56.4%

          \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]

   11. Simplified 56.4%

       \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-178}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-141}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;a \leq 1700000000000:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+158} \lor \neg \left(y \leq 7.6 \cdot 10^{+69}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -3.7e+158) (not (<= y 7.6e+69)))
   (* y (- (* x z) (* i j)))
   (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -3.7e+158) || !(y <= 7.6e+69)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	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) :: tmp
    if ((y <= (-3.7d+158)) .or. (.not. (y <= 7.6d+69))) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    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 tmp;
	if ((y <= -3.7e+158) || !(y <= 7.6e+69)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -3.7e+158) or not (y <= 7.6e+69):
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -3.7e+158) || !(y <= 7.6e+69))
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -3.7e+158) || ~((y <= 7.6e+69)))
		tmp = y * ((x * z) - (i * j));
	else
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -3.7e+158], N[Not[LessEqual[y, 7.6e+69]], $MachinePrecision]], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.70000000000000011e158 or 7.60000000000000055e69 < y

   1. Initial program 62.0%

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

   3. Taylor expanded in y around inf 77.0%

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

      1. +-commutative 77.0%

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

      2. mul-1-neg 77.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 77.0%

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

   5. Simplified 77.0%

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

   if -3.70000000000000011e158 < y < 7.60000000000000055e69

   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 y around 0 67.0%

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

   5. Simplified 68.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+158} \lor \neg \left(y \leq 7.6 \cdot 10^{+69}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 68.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+130}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-6}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -8e+130)
   (* b (* c (- (/ (* t i) c) z)))
   (if (<= b 3.8e-6)
     (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
     (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -8e+130) {
		tmp = b * (c * (((t * i) / c) - z));
	} else if (b <= 3.8e-6) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	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) :: tmp
    if (b <= (-8d+130)) then
        tmp = b * (c * (((t * i) / c) - z))
    else if (b <= 3.8d-6) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    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 tmp;
	if (b <= -8e+130) {
		tmp = b * (c * (((t * i) / c) - z));
	} else if (b <= 3.8e-6) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -8e+130:
		tmp = b * (c * (((t * i) / c) - z))
	elif b <= 3.8e-6:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -8e+130)
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(t * i) / c) - z)));
	elseif (b <= 3.8e-6)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -8e+130)
		tmp = b * (c * (((t * i) / c) - z));
	elseif (b <= 3.8e-6)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -8e+130], N[(b * N[(c * N[(N[(N[(t * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e-6], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.0000000000000005e130

   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 b around inf 74.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 74.9%

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

      2. *-commutative 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in c around inf 77.3%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\frac{i \cdot t}{c} - z\right)\right)} \]

   if -8.0000000000000005e130 < b < 3.8e-6

   1. Initial program 73.8%

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

   3. Taylor expanded in b around 0 72.2%

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

   if 3.8e-6 < b

   1. Initial program 70.8%

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

   3. Taylor expanded in y around 0 71.1%

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

   5. Simplified 72.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+130}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-6}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -9 \cdot 10^{-77} \lor \neg \left(j \leq 1.8 \cdot 10^{+125}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -9e-77) (not (<= j 1.8e+125))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -9e-77) || !(j <= 1.8e+125)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	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) :: tmp
    if ((j <= (-9d-77)) .or. (.not. (j <= 1.8d+125))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    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 tmp;
	if ((j <= -9e-77) || !(j <= 1.8e+125)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -9e-77) or not (j <= 1.8e+125):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -9e-77) || !(j <= 1.8e+125))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -9e-77) || ~((j <= 1.8e+125)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -9e-77], N[Not[LessEqual[j, 1.8e+125]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -9.0000000000000001e-77 or 1.8000000000000002e125 < j

   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 a around inf 47.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 47.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 47.2%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 47.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   6. Taylor expanded in c around inf 38.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -9.0000000000000001e-77 < j < 1.8000000000000002e125

   1. Initial program 68.1%

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

   3. Taylor expanded in b around inf 47.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 47.0%

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

      2. *-commutative 47.0%

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

   5. Simplified 47.0%

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

   6. Taylor expanded in t around inf 26.1%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 26.1%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 26.1%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9 \cdot 10^{-77} \lor \neg \left(j \leq 1.8 \cdot 10^{+125}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 22.7% 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 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 a around inf 36.4%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 36.4%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 36.4%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 36.4%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 36.4%

      \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

5. Simplified 36.4%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

6. Taylor expanded in c around inf 20.6%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

7. Final simplification 20.6%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
8. Add Preprocessing

Developer target: 58.9% 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 2024130 
(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)))))